modify iPhone 7 plus battery

I'm fairly confident you're not going to be able to use any BMS, or Battery Management System in an iPhone 7 unless it comes from an iPhone 7. That means you'll have to clip the terminal strips from the little circuit board that's mounted on the battery and attach them directly to the plus and minus terminals of the cell you want to use - after removing the BMS from it as well. If you do use the original BMS, you might want to use a device programmer like the Qian Li iCopy or the JC VS1E to clear the cycle count and health percentage; otherwise it will still read whatever numbers were there when you took it off the old cell.

It's hard to say if the difference in mAh values will affect anything or not. The phone uses voltage and temperature readings to determine the charging rate and decide when to stop charging, so that should all work correctly, but I doubt anyone knows for sure if your battery charge percentage and/or battery health percentage will be reported correctly. There are plenty of sites that claim to sell high mAh batteries, but it's who knows if they've modified their BMS to compensate for the difference or not; they certainly don't include any warnings that your percentages might not read correctly.

While you can solder the terminal strips, spot welding is by far the preferred method. Heat is the mortal enemy of Li-Ion batteries and the spot welder transmits far less heat to the cell than soldering does. If you do solder them, you might consider clamping a pair of hemostats between the cell and the part you're soldering to act as heat sinks to help keep the heat from getting to the cell. Of course you'll want to work as quickly as possible and use the least amount of solder you can so it doesn't hold the heat there in the molten metal.

Sorry I don't have a definitive answer for you, John, but that's about all the information I can give you to help out. How are you planning on attaching the modified battery to the phone, since it obviously won't fit in the same space as the original.

Good luck with your little project, and be sure to come back and let us know how it all turns out. Tell us if the charge and health percentages seem to work after you swap out the cell; we'll be interested in what you find.