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If you joined the company through local transfer i.e. you were in Saudi already, then they are obligated as per principle to give you a transfer.  However this is NOT required by labor law and the sponsor can refuse to give it to you.  The only way you can fight on the principle is by filing a case in labor court which will cost time and money but you might be able to get the outcome you need.   There is NO other way as they have already issued final exit and no transfer is possible when you have final exit.

Transfer without consent is only possible in a few cases like moving from an employer in the red zone of nitaqat to one in the yellow etc.

Hi, can you update about any progress. I am facing the same situation.

you have to do final exit

Unfortunately, you have to comply with the final exit visa as it's your sponsor right, from my previous experience, those kinds of conflicts could be solved by negotiations. as long as the employer does not violate the labor code, he is in good standing in situations like this.
all the best!
Regards,