A UTI in a cat is prime reason to prompt them to stop using the litter box. They pee, the higher alkaline urine burns and hurts them, they think the litter box is to blame so they try another spot to pee. Now, this does not sound like your situation because your cat is using one other spot but it's still worth a check at your Vet's.
There are innumerable other reasons for your cat to stop using a box. A spat with one of the other cats, the other cat has a UTI and the box doesn't smell right anymore, something happened when he was down there once and it frightened him. I doubt you will ever learn the reason and some things just aren't worth the trouble. Far easier to get more litter boxes, ideally at least two more, one per cat. Plus many of us have an extra.
I'd put the new litter box where your cat now chooses to make his bathroom and hope to get him using it there before trying to move the box.