How to fix a RJ45 connector patina without poison or with common tool?
The best way to go is to cut the cable and put a new connector.
To do so you need a specialized crimping clamp and some connectors. Usually, the way it works is that you insert the cables (without stripping them) and the connector has small blades that will pierce through the insulation while crimping.
Gluing probably won't work or you need some very expensive conductive adhesive.
Trying to remove the patina (oxide layer) also is not so useful as what matters is the connection within the contact.
Trying to solder within the connector will melt the housing.
Given the price of the crimping tool, you definitely rather buy it than cutting/soldering the cables together, it will make your life easier, do a better job and it will be a useful tool to have.