The photographer asked my girlfriend to take photos for free, but the photos should be his work. Is this good?

This is a normal photography behavior before the two sides became famous, which is called "double exemption".

Take what you need. You think the photographer is good enough, better than you pay someone else. Why not get it for him?

The photographer thinks your girlfriend is better than the model he paid for. Of course he would like to take a photo with your girlfriend.

If both parties are satisfied, they will not spend money, and their efforts will be rewarded accordingly. Good thing!

If everyone is famous in the industry, let's say it by the agent!