How does one pray the Witr prayer after sunrise if it was missed, given that it consists of three rak'ahs, taking into account that the Prophet (peace be upon him) used to pray "twelve rak'ahs" if he missed the night vigil (qiyam al-layl)?

The aforementioned Hadith is authentic, and it indicates the desirability of maintaining awrad (regular devotional practices) and making them up if missed. Some scholars used it as evidence that Witr (the odd-numbered prayer after Isha) should not be made up in its original form, but rather by adding one rak'ah to it, based on the Hadith of Aisha (may Allah be pleased with her) that when the Prophet (peace and blessings be upon him) was overcome by sleep or pain and missed the night vigil, he would pray twelve rak'ahs during the day. The more preponderant opinion is that it should be made up in its original form, based on the Hadith of Abu Sa'id (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "Whoever sleeps through his Witr or forgets it, let him pray it when he remembers it." In summary, for someone who missed Witr, it is more preferable for him to make it up in its original form, and if he makes it up by adding one rak'ah to it, that is also good.