A nice point. Send the person who retook it all the bills incurred in vet's fees , feeding it to keep it healthy and add a bit for boarding and invite them, in the alternative, to waive any rights which they now claim to have in it and restore it to you.
As to the law, an owner retains their rights of ownership in property forever until such time as they transfer ownership [there are some provisions in Acts of Parliament that affect this e.g where goods for repair are left uncollected for a certain period the repairer may dispose of them].But, if they have intentionally abandoned it, giving up their interest by declaring, in their action in abandoning it, that they no longer want oi have ownership they seem to me to have no right of reviving that ownership as against the person who takes possession of it, certainly where that person has acted to his own detriment in respect of it as though he were owner (as by spending money on it to preserve or restore it)
The original owner may argue that he never intended to abandon it. Given the length of time, consider what would have happened if your friend had taken it to an animal charity for them to care for.By now the animal would have been rehomed.The charity might have enquired then of the original owner, if found, what he wanted to do with the cat.He would evidently have replied 'You keep it, I can't ' and the cat would be sold or given to a new owner. .