Partner has moved out of rented flat, what can I do?

If your partner is on the signed lease agreement, he is still responsible for his portion of the rent until the lease is up. The only other viable option you have is in getting him to agree to advertise for another roomy. That way you could get someone else in there to share the rental burden. Just make sure to check with your landlord either way. Some places are more than happy to work with sublets, but for others it is against policy. Good luck!