Can you change a student visa into a working visa before graduating?

Hey everyone,

So, I've jut received a job offer after graduating next year April. However, the job requires me to move cities and HR told me it would be better to apply for a work visa in January, before I move in April.

But I am still on a student visa, and as I've said before, I will only be graduating in April.

Can I actually change my visa from student to work visa while still being a student?
Or do I have to wait untill after graduation?

Thank you very much in advance for any answers!