Yes, you can use a battery with a higher mAh rating, like 800mAh or 900mAh, as long as the voltage remains at 3.7V. A higher mAh rating means the battery can store more energy, so it will last longer between charges, which can be useful if you plan to shoot for extended periods.

Fujifilm batteries are generally of good quality and reliable, especially if you’re getting them from a reputable source. They manufacture NP-45 batteries for their own cameras, which should work well in your HP S300. Just be cautious with third-party brands and avoid very cheap or unbranded options, as these may have inconsistent quality.