Q: What is the rule and role of سمع الله لمن حمده when standing up from Ruku? Does imam read ربنا لك الحمد does muqeem also say سمع الله لمن حمده and ربنا لك الحمد does muqeem just say ربنا لك الحمد, does muqeen say any of it loudly if he wishers? Or must any of this be said softly? Must the imam stand after saying سمع الله لمن حمده while people say ربنا لك الحمد and pause thill people in the back say what they need to say and then go down? What must the imaam do? What does Muqeem (follower) do? 

A: The imam should not wait, he should go directly into the Sojood posture after saying سمع الله لمن حمده. If the imam wishers to say and say ربنا لك الحمد although accepted, however, as per Ahnaf, it is not Sunnah for the imam to wait and recite it. Thus, it is best for the imam to go into sojood. The imam reciting ربنا لك الحمد would not negate or create a deficiency in the the salah.

(If an imam is speedy and this would offend some of the musallen, he may recite ربنا لك الحمد to control his speed as he gradually begins to eliminate this speedy practice.) 

As with the Muqeem, they would say ربنا لك الحمد softly. The entire Musjid need not hear it. Softly is defined as he must be able to hear it, and not interrupt others. Prayers and praying are not to be used as a weapon of disturbance. It is to be connected to Allah (SWT) and doing so in a manner that helps others accomplish their duties in a nice manner.

Allah Certainly Knows Best. 

P.S. Please refer to Biday us Sanai for more detail.