How to change Badge SAK

Hello, I have a Project where I need to clone an RFID badge (for a parking entrance). I try it with RC522 module but it dosn't work. The 2 badge have the same UID but not the same SAK. The original one get SAK 88 and all new have SAK 08.

Does problem come from SAK?
Is it possible to change SAK?

If you have any idea do not hesitate to send them to me, it would be very useful to me.

Thanks all for help

If you have an idea with an other module you can also suggest it to me

Not specific. Does the MFRC522 module actually read all the data from the tag?

I can read this on new badge :
Card UID: C5 89 19 3D
Card SAK: 08
PICC type: MIFARE 1KB
Sector Block 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 AccessBits
15 63 00 00 00 00 00 00 FF 07 80 69 FF FF FF FF FF FF [ 0 0 1 ]
62 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00[ 0 0 0 ]

and for the old (the one i need to clone i just have :
Card UID: C5 89 19 3D
Card SAK: 88
PICC type: MIFARE 1KB
Sector Block 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 AccessBits

Don't you think that they would make it extremely difficult/impossible to copy cards to prevent fraudulent activity?

Maybe this type of card but in RC522 i have clone module that can copy UID information