The easiest way to solder multi pin connector?

First, learn to solder. I bet there are some videos on YouTube. Then get the right equipment and practice until you get the hang of it. 

@russ69 ,

I’d second that. There’s nothing like practice when it comes to soldering.

Cleanliness is crucial. Otherwise the solder doesn’t stick well.

I used isopropyl alcohol when replacing the 3.5mm jack on my Sennheiser headphones.

Here's the first one of a nice video series on YouTube I found both helpful and informative.

A temp controlled device is essential for these larger items.

I use a combination of pumps and solder wick. 

Get into the habit of using needle nose pliers to move those headers, not your bare hands. :D

If you want to do this right, then get the desoldering gun in the link below. Trying to use a manual solder sucker or braid can be difficult and leads to mishaps.  This desoldering gun makes easy work of it. If you plan to desolder more in the future, then it is a must have purchase. First use your soldering iron to reflow the solder pads you plan to use the gun on. 

OMG, if you don't know how to solder, find a friend that does or just buy a pre-made cable even if it has more wires than you need.