Yes, your understanding is correct, because there are two scenarios for the issue mentioned:
- The time for the prayer has begun and fulfilling the condition of purifying himself with water is not possible, and if he tries to acquire water or collect wood to heat it and the like, the time for the prayer will end. Then in that case tayammum is sufficient for him to pray, whether that is at the beginning of the time for the prayer or the end, because Allah, may He be Exalted, says: {Prayer is prescribed for the believers at specific times } [An-Nisa’ 4:103]. And because he has no water available to him or he is unable to use it, and thinks that it is most likely that the time for the prayer will end before he can obtain water (that he can use).
- He wakes up at the end of the time for the prayer, and he has water and is able to use it, but he fears that the time for the prayer will end if he uses the water. In this case, he must still purify himself with water, and it will not matter if the time for the prayer ends in this situation, because he is excused for the time that he missed from the beginning of the time for prayer, as he was asleep. Rather in his case the obligation to pray begins from the time when he woke up.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said in Majmu` al-Fatawa, 21/471:
With regard to the traveller, if he reaches the water and the time remaining for the prayer is short, tayammum is sufficient for him to pray according to the view of the majority of scholars. Similarly, if there is a well but he cannot make a rope before the time for the prayer ends, or he can dig for water but the water will not become available until the time for the prayer ends, then in this case tayammum is sufficient for him to pray.
Some of the jurists among the companions of ash-Shafa`i and Ahmad said: he should do ghusl and pray even after the time for the prayer has ended, because he was busy trying to fulfil the condition for praying. But this is a weak view, because the Muslim is enjoined to pray on time in whatever manner is possible. So if the traveller knows that he will not find water before the time for the prayer ends, then it becomes obligatory for him to do tayammum and pray on time, according to the consensus of the scholars, and he has no right to delay the prayer until he reaches water when the time is so short that he will not be able to do ghusl and pray before the time for the prayer ends. Rather if he does that he will be sinning according to scholarly consensus, and in that case if he reaches the water when the time is too short, what he must do is do tayammum and pray on time, and he is not enjoined to use water that could lead to him missing out on praying on time.
This is in contrast to the one who wakes up at the end of the time for the prayer and has water available to him. In this case, he is enjoined to do ghusl and pray. The time for the prayer in his case begins from the time when he woke up, not from the time when dawn broke; this is in contrast to one who was awake when dawn broke or when the sun passed the meridian, whether he is at home or is travelling – for him, the time for prayer begins at that point. End quote.
He also said in Majmu` al-Fatawa, 22/35:
If someone is awake when the time for prayer begins, but water is far away and he will not be able to reach it until after the time for prayer ends, then he must do tayammum and pray on time, according to scholarly consensus.
Similarly, if it is extremely cold and using cold water will harm him, and he is not able to go to the bathhouse or heat the water before the time for the prayer ends, then he should do tayammum and pray on time.
This applies equally to both women and men. So if they are junub and will not be able to do ghusl before the time for the prayer ends, then they should do tayammum and pray on time.
If a woman is menstruating and her bleeding stops during the time for prayer, but she will not be able to do ghusl until after the time for prayer ends, then she should do tayammum and pray on time.
Whoever thinks that purifying himself with water and praying after the time for the prayer has ended is better than doing tayammum and praying on time is misguided and ignorant.
If he wakes up at the end of the time for Fajr and finds that if he does ghusl, the sun will have risen (before he completes his ghusl), then the majority of scholars say that in this case he should do ghusl and pray after the sun has risen. This is the view of Abu Hanifah, ash-Shafa`i and Ahmad, and it is one of two views in the madhhab of Malik.
He said regarding the second view: Rather he should also do tayammum in this case, and pray before the sun rises, as we have discussed above, because doing tayammum and praying on time is better than doing ghusl and praying after the time for the prayer has ended.
The correct view is the view of the majority, because the time for prayer in the case of one who was sleeping begins from when he wakes up, as the Prophet (blessings and peace of Allah be upon him) said: “Whoever sleeps and misses a prayer or forgets it, let him pray it when he remembers it, because that is the start of the time for that prayer in his case.”
Therefore, in the case of one who is sleeping, the time for prayer begins from when he wakes up, and the time before that is not time for prayer in his case.
As that is the case, if he wakes up before the sun rises but is not able to do ghusl and pray until after the sun rises, then if he does that, he is regarded as having prayed on time and he has not missed it. This is in contrast to one who wakes up at the beginning of the time for prayer; in his case the time for the prayer begins before sunrise, and he has no justification for missing the prayer.
The same applies to one who forgets to pray, then remembers it. At that time, he should do ghusl and pray, no matter what time it is, because this is the time for the prayer in his case. So if he does not wake up until after the sun rose – as the companions of the Prophet (blessings and peace of Allah be upon him) woke up after having fallen asleep and missed the prayer during the Khaybar campaign – then he should purify himself completely and pray, even if he delays it until the time of the zenith. End quote.
Shaykh Ibn `Uthaymin (may Allah have mercy on him) was asked: is it permissible for someone to delay the prayer in order to fulfil one of the conditions of prayer, such as if he was too busy looking for water (to purify himself)?
He replied: The correct view is that it is not permissible to delay the prayer from its time at all. If someone is afraid that the time will end, he should pray according to his situation, even if he would be able to fulfil the condition soon, because Allah, may He be Exalted, says:
{Prayer is prescribed for the believers at specific times} [An-Nisa’ 4:103].
That is because the Prophet (blessings and peace of Allah be upon him) defined the times of prayer, which indicates that it is obligatory to offer the prayers on time.
Moreover, if it were permissible to delay the prayer until one has fulfilled the conditions, there would be no point in the prescription of tayammum, because one would be able to obtain water after the time for prayer has ended. There is no difference between delaying it for a long time or for a short time, because in both cases, he will still be praying after the time for the prayer has ended. This is the view favoured by Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him).(Majmu` Fatawa wa Rasa’il al-`Uthaymin 12/20).
And Allah knows best.
