Can you carry your EOSB if your company moved to free zone under a different name?

Hi

I am currently working in an LLC company since 2019.

Recently, the company moved to a free zone with a different name and asked me to sign a letter of agreement to transfer my contract to the new company.

This means that my end of service will be carried forward and paid along with whatever amount in the free zone company. Is this possible legally?

Please, I need your advice urgently.

The mother company and the current company are owned by the same owner.