Can I replace default Dual Shock 4 battery to ant other which has more mAh?

I decided to replace the battery in my Dual Shock 4, because the default is quite weak. After a few hours of using PS4, I get notifications on the screen that the battery is low and I have to charge it.

I read that the default battery has 1000mAh of capacity and I can swap it to another, stronger unit. I looked on the webshops for the new one, but I saw some warnings in descriptions of some batteries, that they are compatible only with DS4 Pro controllers. Is it true? What is the difference between DS4 Pro and the normal DS4. Is the battery socket different?

My controller has id CUH-ZCT2E on the sticker.