The soldering fix is a non-starter. The problem with low cost store own brand "pile 'em high and sell 'em cheap" stuff is that there's next to zero support. You MIGHT strike lucky at www.solenttools.co.uk but I wouldn't hold me breath.
I have been seriously impressed by the spares coverage of Eindhell tools. You do have to dig for the info but it looks like everything is available. Just be sure you record the model number, item code and serial number. They were also sold under the Ozito brand through Homebase when it was briefly run by Bunnings.
https://www.amazon.co.uk/Einhell-Power-X-Change-Cordless-Reciprocating/dp/B089PFRCRC
Rjrj, May 2022