I just want to ask if possible that my employer...

We would like to inform you that according to the Kuwaiti Residence Law, yes, you can transfer with the following documents:
1. A residence request form prepared for that signed by the previous sponsor to concede the new sponsor with approval.
2. Two personal photos, a blue background measuring 4 x 6.
3. The original passport of the sponsored person.
4. The original ID of the sponsored person (for cancellation).
5. Original ID of the new sponsor and a copy.
6. The original civil ID of the assignee and a copy of it.
7. Pay the Medical Insurance fee

You can follow the link to know the procedures Visa Transfer