For this,

You need to go to the Muroor with the following documents
- Dubai Driving License
- No objection letter from your sponsor
- RP copy & ID
- PP Photo

I think you also need a letter in arabic to issue the license, can't remeber. The typing centres near the Muroor will do that.

You need to pay QR.250 using ATM/Bank card

I did this about a year back. I got my Dubai License back.

I hope the rule is still the same.