Answered by Shaykh Hamza Karamali, SunniPath Academy Teacher
I understand that the intention to join prayers must be made at the opening Allahu Akbar or anytime during the first of the two prayers. So, during the second salams of the prayer, one can intend to join the prayers (because one is considered to be in prayer still)?
In the Name of Allah, Most Merciful and Compassionate
The intention for joining prayers early in the time of the first prayer must be made while performing the first prayer, even if this is done while exiting from the prayer. (Tuhfa, 2.395) One exits the prayer by performing the obligatory first salam; the second salam is merely a sunna. It is therefore valid to make the intention to join prayers during the first salam, but not during the second.
And Allah Most High knows best.
Hamza.