When is it prescribed to say, "May Allah hear him who praises Him"? Is it permissible to complete it after rising from rukūʿ due to lack of time, and is there a fatwa from Ibn ʿUthaymīn regarding this?

The place for tasmee' (saying "Sami'a Allahu liman hamidah" - Allah hears those who praise Him) is between the beginning of rising from ruku' (bowing) and straightening up. It should not be prolonged such that it is completed after straightening up. Some scholars consider it insufficient in that case, and this is the madhhab (definition) (school of thought) of the Hanbalis. However, some pardon this due to the difficulty of avoiding it and the frequency of unintentional errors. The takbeer (saying "Allahu Akbar" - Allah is the Greatest) for lowering, rising, and standing should begin with the commencement of the transition and end with its completion. The ruling for tasbeeh (glorifying Allah) and tahmeed (praising Allah) is the same as that for takbeer. A fatwa (definition) has been issued indicating that completing the takbeer, and similarly the tasmee', within the rukn (pillar) being moved into, is permissible. Therefore, the takbeer for moving in prayer from one pillar to another occurs between the two pillars. If one begins the takbeer before prostrating and completes it while descending, there is no harm. Similarly, if one begins it while descending and does not complete it until prostrating, there is no harm.