No. If you have changed employers, you do not need to notify Social Insurance Agency.
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Report a change of employer
Should I notify the Social Insurance Agency of a change of employer?
How will the Social Insurance Agency find out that I have a new employer?
Upon termination of employment (or other relationship with income from dependent activity), your employer must deregister you from the register of insured persons. The employer will do so within eight days from the termination of the employment relationship concerned.
If you are re-employed, your new employer must register you as an employee again. This should be done at the latest before starting the performance of your activity.
We recommend that you report the starting of a new job only if you received unemployment benefits after the end of your employment and the support period has not yet ended.
At the moment of starting a new job, you are no longer entitled to unemployment benefit, therefore you should report this situation to the Social Insurance Agency within eight days after starting a job, so that you do not have to return the benefit later (in the event that it was paid for the period after you started employment ). You can report the change by phone.