There will be an increase of the mass of the battery when you charge it, though that increase is going to be undetectably small.
I would do the calculation in reverse i.e. start with a fully charged battery and calculate how much it decreases in mass when you run it down. The mass decreases because the battery does work $E$ on the electrons that flow through it and that work is related to the mass lost $\Delta m$ by Einstein's famous equation:
$$ E = \Delta m c^2 \tag{1}$$
We can do an approximate calculation using the information you provided:
Maximum capacity of the smartphone's battery: 2000mAh
That capacity means the battery can supply a current of $2$ amps for an hour, so if the battery voltage is $V$ it can supply a power of $2V$ for an hour and the total energy is therefore:
$$ E = 7200V \tag{2} $$
If we substitute this into equation (1) and rearrange we get:
$$ \Delta m = \frac{7200V}{c^2} $$
Smartphone batteries have $V\approx 4$V and this gives us:
$$ \Delta m \approx 3.2 \times 10^{-13}\,\text{kg} \approx 0.32\,\text{nanograms} $$
This is approximate because the battery voltage isn't constant as the battery discharges so our equation (2) isn't exact. However it gives us a good estimate of how much the mass decreases on discharging and increases again on recharging.