Batteries with side connections to the protection board do not seem to exist, so the original battery flex cable cannot be reused, and you’ll need to solder the new battery in place.

Cut the connector off one wire at a time so you don’t short the battery, strip just a few mm of insulation, twist and tin the wire ends.

Replace the blue plastic cover over the new battery, and seal with Mylar or electrical tape. Be sure to include the foam padding to keep the battery from moving around too much.