Change of type of residence permit

Hi Family!

I am from Ethiopia and I finished school from Corvinus University of Budapest on Septemeber 2018 and have been here in Hungary on job searching and entrepreneurship residence permit since then. I have just found a job and about to reapply for an employment residence and work permit. But one possible issue I have is that I have only 17 days before the expiry of the current residence permit I have and I m concerned if this might affect the procedure of changing the type of my document. 

Is there any specific length of days when the application for the purpose of employment must be submitted for a third country national like myself before the expiry of the validity of my residence permit for job searching or entrepreneurship? I can't find anything on the official website of the relevant authority but am concerned that the office might turn down my application on the basis of not enough time.

I appreciate very much any relevant advice that can help me know what to expect before I visit the office in the next few days. Thank you!!

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