How to fortify damaged power jack connection in a laptop

In order to replace the power jack in your laptop you’ll have to remove the jack from the motherboard as I explained in the previous post: Replacing DC power jack.
While removing the jack you can accidentally pull out the internal copper coating (I’ll call it a sleeve) from the inside of the “+” terminal as it shown on the picture below.

The internal copper sleeve has been removed and cannot be installed back. If you solder the power jack back on the motherboard without this sleeve it might work but the connection between the “+” lead and motherboard will not be reliable.
In the following guide I explain how to fortify a damaged power jack connection. You can use this repair technique in some laptops with similar power jacks.