jremington:
You also need a charger module designed for LiPo batteries to prevent overcharging, and a protection circuit to prevent overdischarging. Otherwise you will destroy the battery very quickly.NiMH cells are much easier to use and tolerant of abuse. They can be trickle charged by a solar cell indefinitely.
He is using a TP4056 charging module, it has built in over charging protection. It's over-discharge protection is set way too low. Using a protected li-ion cell is highly recommended.
LiFePO4 cells are now easily available in the market and in my opinion a better alternative to NiMH cells. They also provide nominal 3.2V for a single cell. He can use a TP5000 module to charge these cells.
If using NiMH cells then it's best to avoid them LSD variants because they don't like trickle charge.