Take both parts of the latch off.

Screw a longer section of wood vertically to the wall with long screws, ideally you can get that into the stud if not use some construction glue to help.

Cut a small section of this wood the same thickness and put it on the door, under the catch, and mount the latch to the wood on the wall. Both of them are reinforced, and moved the same amount away from the wall/door