What should be done with ex-tenant's mail?

Other

The tenant left no forwarding address initially.
The tenant came at some point a month or more after they had left and demanded access to retrieve their mail and claimed there was a very important letter from hospital amongst it. They were declined at this stage as the mail had been taken to another property to start going through it and put "return to sender, addressee has left". Upon returning to that property and checking for a hospital letter, I found none. I suggested to tenant to do mail-forwarding and to give me their address for the rest that we receive until they arranged mail-forwarding. The tenant refused.
I later found out that the ex-tenant had only arranged for a month of re-directing mail as the house started to receive mail for the ex-tenant again.
Since meeting at a preliminary hearing for small claims on either side, I have offered to forward mail now that I have the ex-tenant’s address. However I do not want to do this forever. How long must I continue this for before I can start to put "return to sender, addressee has left"?