Charging with low power

This is a Panasonic document that outlines how to do charging of lithium ion batteries:

https://eu.industrial.panasonic.com/sites/default/pidseu/files/downloads/files/li-ion_handbook_22_10_15.pdf

If there's no temperature monitoring of the cell, you wouldn't try to charge (for the constant current phase) at more than 0.5 to 0.7C, though that would depend on the situation of the battery (if it were wrapped in expanded foam you might want to measure the temperature and make sure it wasn't getting too hot). Charging and discharging are both exothermic (some of the energy going in during charging or coming out during discharge ends up as heat in the battery).

Charging at a lower current will just take longer.

Ambrogio perhaps could have added a third state. As well as the constant current and constant voltage phases, the charger needs to know when to stop. That can be done in a variety of ways, but the most usual is to stop when the current falls to a percentage of the C rate - the Panasonic document gives the range 7%-10%, which in the case of Enricho's 500mAh battery is between  35mA and 50mA. If you don't stop, but try to trickle charge it like a lead-acid battery, you'll overcharge the cell. There's some leeway, the manufacturer includes a chemical buffer that means you can go beyond the 100% capacity point without damage, but go too far beyond and you'll seriously degrade the cell. If you can get the data on the charger, look at the data for the end point and see if it's reasonable. If you can't get the data, you maybe could try charging the cell and measuring to see at what current the charging stops (and stop it yourself if it goes on too long, obviously), but you'd need a means of doing that that didn't interfere with the charging; an ordinary handheld meter on a current range has a high enough voltage drop that it interferes with the charging - some of the better bench meters could do this, but you probably don't own one.

This is a Panasonic document that outlines how to do charging of lithium ion batteries:

https://eu.industrial.panasonic.com/sites/default/pidseu/files/downloads/files/li-ion_handbook_22_10_15.pdf

If there's no temperature monitoring of the cell, you wouldn't try to charge (for the constant current phase) at more than 0.5 to 0.7C, though that would depend on the situation of the battery (if it were wrapped in expanded foam you might want to measure the temperature and make sure it wasn't getting too hot). Charging and discharging are both exothermic (some of the energy going in during charging or coming out during discharge ends up as heat in the battery).

Charging at a lower current will just take longer.

Ambrogio perhaps could have added a third state. As well as the constant current and constant voltage phases, the charger needs to know when to stop. That can be done in a variety of ways, but the most usual is to stop when the current falls to a percentage of the C rate - the Panasonic document gives the range 7%-10%, which in the case of Enricho's 500mAh battery is between  35mA and 50mA. If you don't stop, but try to trickle charge it like a lead-acid battery, you'll overcharge the cell. There's some leeway, the manufacturer includes a chemical buffer that means you can go beyond the 100% capacity point without damage, but go too far beyond and you'll seriously degrade the cell. If you can get the data on the charger, look at the data for the end point and see if it's reasonable. If you can't get the data, you maybe could try charging the cell and measuring to see at what current the charging stops (and stop it yourself if it goes on too long, obviously), but you'd need a means of doing that that didn't interfere with the charging; an ordinary handheld meter on a current range has a high enough voltage drop that it interferes with the charging - some of the better bench meters could do this, but you probably don't own one.