Can a 5200 mah battery replace a 4400 mah battery?

Yes - so long as it's (a) physically identical in sizeand (b) the same voltage as the one it's replacing. The mAh number is the capacity of the battery - the 5200 mAh one will simply take slightly longer to charge than the 4400 mAh. I replaced the 950 mAh battery in my phone with an 1100 mAh one over two years ago - and it's never given me any problems. It just takes about 10 minutes longer to charge from completely flat.