May an imam lead the Friday prayer in two places on the same day?

Not at the same time. The imam leads the prayer as someone standing with the congregation, and he can only do that in the place where he himself is.

The Friday prayer is a prayer of the community. Believers set their work aside, gather in one place, listen to the sermon and pray together behind an imam. The verse above calls for exactly this.

The imam is not merely a speaker. He stands in front of the worshippers, and they follow each of his movements. He bows, and they bow. He raises his head, and they raise theirs. The hadith above describes this order. It assumes that the imam is truly present with the people who follow him.

So the answer is simple. No one can stand in two places at the same time. Therefore no one can lead the prayer in two places at the same time either.

What matters is that every congregation holds its Friday prayer. The call of the verse applies to all believers wherever they live. Each community gathers in its own place and prays there behind the one who stands with it.