Need help diy a power bank

The battery in the power bank seems to be of the flat pouch type. That one would be a Li-Ion cell with a nominal voltage of ~3.7 V (label is possibly on the reverse side of the battery.
This pouch should be replaceable by another Li-Ion cell that fits the case.

1. If you do so, you'll have to connect the remaining 3 batteries in parallel to achieve the 3.7 V (approx.). In a series connection the battery voltage is way too high.
2. Cutting the battery stack may be straightforward. Soldering Lithium batteries is not recommended. They easily overheat and can catch fire. Although you'll be able to find "instructions" on how to solder these batteries, it really is not recommended. The correct way is by spot welding which requires a special spot welder. If you are lucky there will be short strips of nickel tabs left over from the original weld after cutting the stack. In that case you can solder to these tabs. Works fast to prevent the heat of the soldering to enter the batteries.
3. Last not least you'll have to fit the new battery mechanically into the case of the power bank - or find a new, bigger case.