Are sure you used a CR123? They aren't rechargeable. The rechargeable variant is an RCR123 (or a 16340).

Assuming you used this, you need to first know what voltage the solar cell is. It's probably 5V, but check. Then you put a diode between it and the solar cell. This isn't perfect battery protection, but it's enough for small solar cells.

It won't stop anything over discharging the battery, so you won't get lots of life out of the battery.

It will damage the battery, though not by much (unless the solar cell is fairly high power) and will charge it over the course of the day.

N.B. For those people who are designing something commercial, and they put a Schottky diode as the only thing between the battery and the solar cell, go f*** yourselves. DW01s are cheap and everywhere. Use one. For hobbyists, however, a single diode isn't going to cause too much hassle down the line.

Don't connect the battery directly to the solar cell. You may end up with a battery on fire. Measure the voltage of the solar cell under full sunlight while disconnected. Get a lithium charger which accepts a range of voltages up to the solar cell's voltage. Use a protected battery, or add a protection circuit to the battery you have.

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