Hi,
I bought a property with a friend several months ago, now I would like to move with my boyfriend, we were thinking to rent a place together and the money I would get from my room would basically pay the rent in the place I would share with my boyfriend while I will keep paying my share of the mortgage as usual. Would my friend who owns the flat with me have any claim on the money I make out of my room?

Certainly not! It's still your house, even if you are not living in it. He has the whole house to himself, and you are still paying the mortgage. You have a right to do what you want with your half of the house. Why do you have to pay rent to your boyfriend, you already pay for the mortgage on your house. He should let you stay rent free!