So I recharged my new battery before reassembling my player without any problems. The battery works perfectly! But it was a pain to reassemble my player lol! To be able to close the back panel I was obligated to remove the blue rubber protector that is between the hard-drive and the battery normally... Even without it I had to use a little bit of force to close it!
Beside that all works well
! Tomorrow I will make a little test (or more) to know the autonomy of this new battery and I will post my results.