Working while waiting for Permesso di Soggiorno

Hello all,

We have a bit of complicated case, Me and my daughter have both Turkish and German passports, my wife has only Turkish passport.

We moved to Italiy last 20 September 2023. Me and my daughter applied and got our Codice Fiscale and Residency and adress from the comune.

My wife has a 5 year Shengen visa so she had to wait 3 months to be able to apply to Permesso di Soggiorno. We collected all the documents (after some visits to the questura. She will apply as my wife (married for 13 years). So when the time to apply has come we took the documents to questura and they looked and said it was ok and they will call us to come and apply for the permesso (in 40 days they said - you think this is normal? It has been 18 days and we haven't got a call) The police put a date and a sign on the document, said that this is the start date of the applying.  So we are still waiting for a call or a message from the questura.

The main question is, my wife got a job in an Agrovilla as an assistant cook and will start in april 2024. Can she work while waiting for permesso? Do we need to change the application? Moving to another state (From Umbria to Toscany) affect the application?

Thanks for anyone replying.

Feel free to ask for details.