Although I have no doubt JB or the other recommendations would work,
I'd just take it to a shop that specializes in aluminum welding and
have them do it. I'vd had work like this done at my local, favorite
welding and fabrication shop (but they are experienced with boats and
motors). They can not only do a definitive, permanent fix, but if you
want, can grind it smooth so if you want to re-paint as good as new,
you can. If you do a different fix and it doesn't work for some
reason, you'll just have a bigger mess to clean up before a weld can be
done.

Just make sure they're familiar with the inner workings of an outboard
L/U so they don't mess anything up. But this issue is not uncommon and
you'll find a shop familiar with it, I'm sure. - call around a bit. I