Non-standard method, but it should be strong:
The idea here is to fasten the striker into something solid (the wood pillar) on the left) and not to the damaged door frame.
Remove wood from pillar so it is flush with the frame.
Cut 5mm thick sheet metal into a shape that makes a striker, fasten to pillar with screws ("x")
Replace the wood that was cut off from the pillar, and do some finishing.
As an example of a related thing I did:
It was a very old door, difficult and expensive to replace. One day, thieves broke in. That's how I discovered the lock side of the door was actually full of holes, which had been plugged with plaster over the decades (probably centuries) and painted over. It was well done, with who knows how many coats of paint on top, so I didn't see it, but the lock was screwed into plaster, so it broke easily.
Since the back of the door was flat, I simply reinforced the whole door with plywood, and fastened the lock into that with carriage bolts.
The idea is to not fasten the thieves' target to a fragile repaired area. This allows to make an aesthetic repair without worrying too much about strength.