Is it permissible to transfer the intention of following a congregation from one to another, without interrupting the prayer, if the worshiper joined the first congregation at its end, and then a second congregation was established?

Whoever joins the congregation in any part of its prayer before the Taslim has attained much good, and he enters with the Imam even if it is during the sitting for the Taslim.

There is no harm for a worshipper who has caught part of the prayer to move to another congregation without repeating the opening Takbir, and his prayer is valid according to some scholars. Ibn Qudamah and An-Nawawi permitted the congregation to move due to an excuse.

However, it is safer to repeat the prayer and not to do that in the future. Instead, one should complete their prayer individually, or say the Taslim and then join the other congregation.