mac Mountain not working after installing linux

Hello everyone

i will try to explain as easy as i possible , and excuse my language 😀 .

the problem started when i installed Fedora 23 on my macbook pro 2012 HD , the total HD is 750 GB .

i used 120GB for fedora , after installing fedora with reFindit (dual boot) the mac os not working any more .

i checked the partition type and in gparted it's said (unkown system type) ???

i changed the system type by using gdisk to HFS and this is screenshot from gdisk it's said the system type is HFS already

, so to make sure i used testDisk also to check the system type and it's gives me Linux type !!!!!

i tired to recover some data from the partition by using photorec (attached with testDisk) and it's really gives some of my pic from the mac partition

so please help me to fix the problem and re-using the mac os without formating any data

note : this is the screenshot when i try reboot the laptop showing these options :-

^^ first screen after boot

----- when choosing mac -----

thank you