'Student' Iqama sponsorship transfer process. Help needed.

Congratulation for getting a new job. In your case, your father is your sponsor/kafil. He will write a letter directed to this company saying that he has no objection that his son takes transfer to them. Just google sample Khitab Tanazul from father to son. (خطاب تنازل )

Thanks for the response I haven't had any luck yet finding a sample Tanazul, my Arabic isn't that great. If it isn't too much trouble, could you possibly share a link?

google.com --> sample خطاب تنازل
or take the service of translation or general services office to write a letter for you.

I got my Iqama transferred last month too. There is no need for a letter. All I had to do was go to Jawazat and get a form from them known as Iqrar Tanazul form. Go to the Iqama transfer section in Jawazat and he will give you the form. Fill it and submit it there itself aong with your father. He will verify your Iqamas, stamp the form and give it to you. You just have to give this stamped form to your new employer. Also you will have to enter your employer name and ID in the form.(Company name and C.R. number as registered in COC).
Your new employer will complete the remaining formalities. You will have to get your medical done too when your new employer says so.
Hope this helps