Praise be to Allah.
Firstly:
One should make sure to do the supererogatory (nafil) prayers at the times prescribed in Islamic teachings. If you miss a prayer, what is recommended is to make it up, whether you forgot it or were distracted from doing it, or you entered the mosque when the iqamah had already been given for the obligatory prayer, so it was not possible to offer the regular sunnah prayer that comes before it. That is because of the hadith of Umm Salamah (may Allah be pleased with her), according to which the Prophet (blessings and peace of Allah be upon him) used to pray two rak`ahs after `Asr. He was asked about that and he said: “O daughter of Abu Umayyah, you asked about the two rak`ahs after `Asr. Some people from Banu `Abd al-Qays came to me, and they distracted me from praying the two rak`ahs that come after Zuhr; these are they (i.e., I prayed them now).” Narrated by al-Bukhari (1233) and Muslim (834).
This is the view of the Shafa`is and Hanbalis. See the answer to question no. 114233.
Secondly:
It is not valid to combine the intentions for Duha prayer and a regular Sunnah prayer, because each of these two prayers is done for its own sake, so they cannot be put together.
This is the principle with regard to combining acts of worship. Sunnah acts that are done for their own sake cannot be combined, unlike when the intended purpose is doing the action only.
Shaykh Ibn `Uthaymin (may Allah have mercy on him) was asked: Can I combine the intention of fasting three days of the month with the intention of fasting the day of `Arafat, and will that lead to a double reward?
He replied: Combining acts of worship falls into two categories:
One category is not valid. This is when the act of worship is done for its own sake or is connected to another act of worship. In this case, acts of worship cannot be combined. For example, someone misses the Sunnah prayer of Fajr and is not able to do it until the sun rises, and the time for Duha prayer comes. In this case it is not valid to offer the Sunnah prayer of Fajr and intend to also include Duha prayer, or to offer Duha prayer and intend it to include the Sunnah prayer of Fajr, or to combine them both, because the Sunnah prayer of Fajr is an independent action and the Sunnah prayer of Duha is an independent action, so one of them cannot include the other.
Similarly, if an action is connected to what comes before it, it cannot be combined with something else. So if someone says: I want to intend when praying Fajr to include both the obligatory prayer and the regular Sunnah prayer, we say: that is not valid, because the regular Sunnah prayer is connected to the obligatory prayer, so it cannot take its place.
The second category is when the aim of the act of worship is simply to do an act of that nature, and doing that act of worship is not for a specific purpose. In this case, it is possible to combine acts of worship. For example, a man enters the mosque when the people are already praying Fajr. It is well known that when someone enters the mosque, he should not sit down until he prays two rak`ahs. If he joins the imam in offering the obligatory prayer, that will count for those two rak`ahs. Why is that? It is because the aim is to pray two rak`ahs when entering the mosque. Similarly, if someone enters the mosque at the time of Duha and prays two rak`ahs intending them as Duha prayer, that will suffice for the two rak`ahs of greeting the mosque (tahiyyat al-masjid). But if he intends both of them together, that will be better. This is the guideline on combining acts of worship.
In the case of fasting, when it comes to fasting on the Day of `Arafah, for example, the aim is that on that day one should be fasting, whether you intend it as one of the three days that you fast every month or you intend it as being for the Day of `Arafah. But if you intend it as being for the Day of `Arafah, that will not count as one of the three days, but if you intend it as being one of the three days, then it will also count as being for the Day of `Arafah. And if you intend both of them at the same time, that is better.(Liqa’ al-Bab al-Maftuh, 51/15).
Thus you will realize that it is not valid to combine with one intention Duha prayer and Witr or qiyam al-layl, if you missed the latter and are making it up during the day.
Shaykh Ibn `Uthaymin (may Allah have mercy on him) was asked: Can Duha prayer be combined with making up the night prayers and Witr, and should the recitation be done out loud or quietly?
He replied: As for Duha prayer, it should be offered at its time, but Witr and the night prayers can be made up before that. If you are making up Witr during the day, then it should not be odd-numbered; rather it should be even-numbered. So if you usually pray Witr with three rak`ahs, you should pray it with four, and if you usually pray Witr with five rak`ahs, you should make it up with six, saying salaam between each two rak`ahs.(Fatawa Nur `ala ad-Darb).
And Allah knows best.
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