@Mydoghasbettereyebrowsthanme, I used to be a housing support worker, so know some of the basics.
If you have a joint tenancy, I'm 99% certain that you are "jointly and severally" liable, ie the LL can come after either of you or both of you for any debt.
Have you got a fixed term tenancy, ie reviewed every year or whatever the period is, or has the LL just let it run on without renewing it (known as a periodic tenancy)?
If it's a periodic tenancy, either of you can terminate it by giving the required notice. So, when you're ready to go, giving notice to the LL will end the tenancy and your liability for any rent or other charges after the notice period has ended. You won't be responsible for any rent debt he accrues by remaining in the property.
However, if the LL is a golfing buddy, it might be an idea to explain that you don't know if DH will want to remain there as a sole tenant, so that he gets the chance to stay there if he wants to. I'd do that in a separate letter, to keep that a totally separate matter.
In terms of timing, I'd suggest not giving notice until you're ready to move, to avoid any unpleasantness between DH finding out and you actually moving.
Fixed term tenancies are a bit more tricky. It depends on whether it includes a "break clause", which gives you the right to end it early. If so, you can give notice but the notice period can vary and the clause may say that notice can only be given after a certain point in the term. In that case, you need to try and time your move after that date.
If it doesn't have a "break clause", then you are jointly and severally liable for the rent for the remainder of the term of the tenancy. In an ideal world, you'd synchronise leaving as close as possible to the date that the current tenancy ends.
There's probably someone on here who's a housing specialist who can help, but if not I'd be happy to take a look at the tenancy agreement.