to do it right you should remove and re apply fresh solder (and flux)

if you just reflow you are adding alot of old oxidization and contamination to the joint, and it probably will not be any better than what you started with

if you add on top, you still have the problem above + you will most likely have way too much on it risking shorts and bridges

(there is some chemical sciences behind all of this if you feel like looking it up)

as far as the connector itself, i dunno ... i have not done this repair yet