Li-ion battery compatability

My wireless Playstation 3 controller uses a 3.7v 610 mAh Li-ion battery and I was wondering if I can replace it with a 3.7v Li-ion bettery that has a higher mAh rating to get longer usage out of it. The stock battery's model number is LIP1359 and it has a maximum charge current of .4A and a maximum charge voltage of 4.2v. The battery gets charged by plugging the controller up to the Playstation console so I'm wondering if an aftermarket battery could charge properly. I assume as long as the console doesn't excede the battery's maximum charge current and voltage that it would work fine. Any help is much appreciated. 

Hi,

You are right. mAh only refers to power capacity and how many milliamps the battery can deliver per hour. The more important compatibility measurement is the voltage it supplies. As long as the voltage is close it should work.

Hi John Arbuckle,
Note these points. For charging a battery always 1. the charge voltage should be
higher than the bat voltage here for 3.7v bat it should be in the range of 4.2 to 4.4v.
2. charging current should be fixed at 1/10 of the bat ah to safe guard the bat, here for
a 3.7v 610 ma ie 61 ma is the max charging current that can be supplied to the
bat.
For example for a 6v4.5ah bat you require a charging current of 450 ma
ie 4.5 ah means 4500 ma so 4500ma divide by 10 = 450 ma. like wise calculate the charging current by checking the bat ah which you want to provide and see the max dc current mentioned in the power pack good luck pl review my score.

Your battery quality and capacity checked by its mah if its 3000mah battery then it could run the whole day, but it also depends on the brand, if you use a low-quality battery of 3000mah and compare with Li-ion battery then it will show a big difference.