Firstly: 

Tasmee’ (saying Sami’a Allaahu liman hamidah) when rising from bowing and tahmeed (praising Allaah by saying Allaahumma Rabbana wa laka’l-hamd) when standing up straight are Sunnah and are mustahabb according to the majority of scholars. The Hanbalis are of the view that they are obligatory, and the correct view is that they are obligatory. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said in al-Sharh al-Mumti’ (3/433): 

The evidence for that (i.e., that it is obligatory) is as follows: 

1 – The Messenger (peace and blessings of Allaah be upon him) adhered to that and did not neglect to say Sami’a Allaahu liman hamidah in all situations. 

2 – It is the signal for moving from bowing to standing. 

3 – The Prophet (peace and blessings of Allaah be upon him) said: “When he says Sami’ah Allaahu liman hamidah, say Rabbana wa laka’l-hamd.” 

End quote. 

We have listed tasmee’ and tahmeed as being among the obligatory parts of prayer in question no. 65847. 

Secondly: 

The fuqaha’ are unanimously agreed that the person who is praying alone should say both tasmee’ and tahmeed. So he should say Sami’a Allaahu liman hamidah when he rises from bowing and when he has stood up straight he should say Rabbana wa laka’l-hamd. 

This unanimous agreement was narrated by al-Tahhaawi in Sharh Ma’aani al-Athaar (1/240) and Ibn ‘Abd al-Barr in al-Istidhkaar (2/178). 

But in al-Mughni (1/548) there is something which indicates that there is a difference of opinion on this matter. But they differed as to what is prescribed for the imam and for the one praying behind the imam. 

In the case of the imam: 

The Hanafis and Maalikis are of the view that he should say tasmee’ only, and it is not Sunnah for him to say Rabbana laka’l-hamd. The Shaafa’is and Hanbalis are of the view that the imam should say both tasmee’ and tahmeed. 

The more correct view is the latter one, because it was narrated that Abu Hurayrah (may Allaah be pleased with him) said: “When the Messenger of Allaah (peace and blessings of Allaah be upon him) said Sami’a Allaahu liman hamidah, he would say Allaahumma Rabbana wa laka’l-hamd.” 

Narrated by al-Bukhaari (795) and Muslim (392). 

Al-Haafiz ibn Hajar stated that the fact that it is mustahabb for the imam to say tahmeed may be understood from this hadeeth and others. 

See: Fath al-Baari (2/367). 

In the case of the one who is praying behind the imam: 

The majority of scholars, Hanafi, Maaliki and Hanbali, are of the view that the person praying behind the imam should limit himself to the tahmeed only, and he should not say Sami’a Allaahu liman hamidah. 

The Shaafa’is and Zaahiris (literalists) disagreed with them and said that it is mustahabb for the person praying behind the imam to say both the tasmee’ and the tahmeed. This is the view favoured by al-Albaani in Sifat al-Salaah (135). For more information on their evidence please see the essay by al-Suyooti in al-Haawi li’l-Fataawa (1/35). 

The more correct view – and Allaah knows best – is that of the majority. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said in Liqa’ al-Baab il-Maftooh (1/320): 

When the imam says Sami’a Allaahu liman hamidah, the one who is praying behind him should not say Sami’a Allaahu liman hamidah, because the Prophet (peace and blessings of Allaah be upon him) said: “The imam is appointed to be followed, so when he says takbeer, then say takbeer, when he bows, then bow, when he prostrates, then prostrate, and when he says Sami’a Allaahu liman hamidah, then say Rabbana wa laka’l-hamd.” 

He said, “When he says takbeer, then say takbeer,” and “when he says Sami’a Allaahu liman hamidah, then say Rabbana wa laka’l-hamd”. Thus the Prophet (peace and blessings of Allaah be upon him) differentiated between the takbeer and the tasmee’. With regard to the takbeer, we say what he says, but with regard to the tasmee’ we do not say what he says, because his words “when he says Sami’a Allaahu liman hamidah, then say Rabbana wa laka’l-hamd” are tantamount to saying: when he says Sami’a Allaahu liman hamidah, do not say Sami’a Allaahu liman hamidah, rather say Rabbana wa laka’l-hamd. This is based on the context of the hadeeth in which he says, “When he says takbeer, then say takbeer.” As for those scholars who say that he should say Sami’a Allaahu liman hamidah and Rabbana wa laka’l-hamd, this is a weak argument. No opinion should be accepted in all cases or rejected in all cases until it is measured against the Qur’aan and Sunnah. When we measure it against the Sunnah we see that it is as you heard. End quote. 

See: al-Mughni (1/548), al-Umm (1/136), al-Muhalla (1/35), al-Mawsoo’ah al-Fiqhiyyah (27/93-94). 

Thus it will be clear to you that there is a difference of opinion among the scholars concerning this issue, and it is not strange that some flyers will state the view of some of the scholars. 

And Allaah knows best.