Boba Fett strikes in character, As a result of the attack this character is to be destroyed but

the player uses Old's Ben Spirit - Boba Fett captured this character or not?

A similar question arose re Chewbacca + Old Ben's Spirit and FFG ruled that the damage is still successfully dealt when Old Ben's Spirit is used. Therefore, here, Boba Fett did indeed damage the character (otherwise Old Ben's Spirit wouldn't have been needed to be used), the character is not destroyed and hence capture-able, and so he can therefore capture the character.

Keep in mind that your opponent could choose not to use Old Ben's Spirit and let the unit die instead of being captured.

Keep in mind that your opponent could choose not to use Old Ben's Spirit and let the unit die instead of being captured.

Which would mostly only be useful to either deny your opponent a captured card or if you had something like Return of the Jedi handy.