Fate Transfer moves any kind of counters, not just -1/-1 counters.

This effect may result in useless counters being placed on a creature. For example, if an age counter is moved from a creature with cumulative upkeep to a creature without cumulative upkeep, it will have no effect on the new creature.

If either one of the targets becomes illegal (because it leaves the battlefield or for any other reason) by the time Fate Transfer resolves, the counters don’t move. If both targets become illegal, Fate Transfer doesn’t resolve.