Among the supplications prescribed in the bowing posture is the following narration:

“ʿUqbah ibn ʿĀmir reported: When the verse, ‘So glorify the name of your Lord, the Most Great’ (Q 56:74) was revealed, the Prophet ﷺ said to us, ‘Make it part of your bowing.’” It was related by Aḥmad, Abū Dāwūd, and others with what they deemed a good chain.

That is what he writes, and al-Nawawī says something similar in al-Majmūʿ (3/413): “It was transmitted by Abū Dāwūd and Ibn Mājah with a ḥasan chain.” Al-Ḥāfiẓ Ibn Ḥajar, however, is silent about it in al-Talkhīṣ (1/242). All of their chains include the maternal uncle of Mūsā ibn Ayyūb—his name is Iyās ibn ʿĀmir al-Ghāfiqī—who is unknown, as I have demonstrated in Ḍaʿīf Abī Dāwūd, pp. 152–153, and again in Irwāʾ al-Ghalīl, p. 334. Were the ḥadīth authentic it would indicate that declaring the tasbīḥ is obligatory, which contradicts the author’s statement that it is only recommended. An additional portion of the report will be cited by the author under the heading of prostration.

He then says: “It is recommended for the person praying—whether leading, following, or alone—to say, on rising from bowing, Samʿa Allāhu liman ḥamidah (Allah hears those who praise Him). When he has stood upright… Abū Hurayrah relates that the Prophet ﷺ would say, ‘Samʿa Allāhu liman ḥamidah’ when he lifted his spine from the bow, then, while standing, he would say, ‘Rabbana wa laka al-ḥamd (Our Lord, to You belongs all praise).’” This was narrated by Aḥmad and the two Shaykhs.

I add: It is also documented in Irwāʾ al-Ghalīl, p. 331, with many additional sources.

To reinforce his point that the recommendation includes the congregant, I say: It is evident that this ḥadīth contains two separate remembrances: first, his saying “Samʿa Allāhu liman ḥamidah” when straightening up from bowing; and second, his saying “Rabbana wa laka al-ḥamd” once he is fully standing.