I'll add a little more to this.
We can assume that the Chinese manufacturer has included an adequate protective circuit inside this device.
Right at the Li-ion cell interface.
A circuit that cuts off charge to the cell when maximum cell voltage is reached, cuts off cell discharge when a minimum voltage is reached, limits cell charging current, and cell discharge current, and monitors cell temperature. A device that gets 'HOT' when operating and/or charging is not properly protected. Overcharge protection both overvoltage and overcurrent needs to be AT the CELL.
A circuit that will not continuously trickle charge the Li-ion cell after full charge has been reached as this permanently damages the cell. This applies to solar charging or from another voltaic source.
It will not try and charge the Li-ion cell when the temperature is Freezing or below, even in full sunlight, as this permanently damages the cell. This also applies to solar charging or from another voltaic source.
A 5 volt cell phone charger might be current limited at one amp, two amps, or even 4 amps, but it will not stop charging until the voltage gets to the 5.0 to 5.5 volt it outputs. The cell protective circuit, required by the FTC, stops charging. Cells without a protective circuit are classed as OEM/experimenter products not as end consumer products.
Be aware that elevated temperatures, storage, charging, or use, shorten the lifetime of Li-ion cells. The capacity of the cell will degrade with time, and faster at higher temperatures.
Capacity rating are often expressed in Ch/mah. That's Chinese milliamp hours which are are different than American milliamp hours

The ratio is typically 2.5 to 1.
Also take note that even a great protective circuit in a Li-ion powered product often has BLIND failure modes. Unless the device has a thorough power on self test, a failed function may not be obvious to the consumer/user. When the overvoltage charge protection dies will it not take a charge or will it just keep on truckin?
The device posted in this thread is a bargain at $20, even better at $15.
You couldn't build one for that. Used with care it could be a life saver.
Don't break the solar cell, and don't abuse the device. Electrically or mechanically.
It's Chinese, so buy it before inauguration day or it may cost a lot more.
Test question

Does the term LiPo commonly used for flat pack batteries refer to the totally dry Lithium Polymer chemistry, or to a standard Lithium-Ion cell in a soft Polymer package instead of a steel shell?