while the prospect of desoldering the old and replacing the jack is rather daunting and kinda hard to do if you dont have honed SMD skills and equipment, actually opening the book and resoldering the connection , (solder weld) is pretty rudimentary if you have a decent fine point soldering tool ,,, i wouldn't advise trying it with a kludgy soldering gun or iron on which the tip is orders of magnitude larger than most of the SMD components on the motherboard
i agree with Michael above , the “fix” here is pretty useless without even the physical dimensions of the battery , or removing the tape obscuring the numbers on the existing battery, so we might have some hope of referencing one before tearing apart a device and having it sit while a replacement battery is coming ,,,, remember some of us live in very remote areas where it takes quite a while to get parts
