No harm to cell phone battery.
elaborate
1. As long as the output voltage of the mobile power supply matches the input voltage of the battery, the output current is less than or equal to the input current will not cause damage.
2. If you use a low current output to charge a high current battery, the only effect is that the charging speed is slower. But it's good for battery life.
3. If high current\/high voltage is used, the battery may burn.
4. If low voltage is used, power supply will fail.