If you increase the capacity of the cells, a well-designed charging circuit should handle them just fine, increasing the charge time as necessary. Decreasing the capacity would be more dangerous because the charge current would be too big for the new cells.
Whenever this particular circuit is well-designed or not is quite impossible to tell from the photo.
Some battery packs also estimate the amount of charge remaining in the cells. For such estimation current cell voltage is not enough, because individual cells have slightly different curves of voltage vs charge. To improve the estimate, your battery pack may use a hardcoded capacity value and/or estimate it during previous charge/discharge cycles.
Hopefully, this charge estimation doesn't affect the charge process, otherwise your cells may stop charging prematurely and you will never use their full capacity.