What should a person do if the Friday sermon in one mosque coincides with the adhan of another mosque, and in which of them should he pray? And what should he do if he begins praying in one mosque and then another mosque issues the adhan during his prayer?

There is no objection to the multiplicity of Friday prayers in a single city when there is a necessity, such as the old mosque being too small or fear of strife. You may pray in either of the two mosques. It is preferable to choose the mosque with the larger congregation, especially if its imam is proficient in the Quran and sound in creed, and his sermons include admonitions. If you have already entered the prayer and hear the adhan or sermon from another mosque, you must continue your prayer and it is not permissible to interrupt it.