ARC Change of residence purpose

I graduated from uni in June, got a 6 month extension to find a job, now I got admitted to a master’s program and want to change to a student arc again. The immigration agency told me to go to mofa and MOFA to immigration. Both agreed that If each one couldnt find a solutions I should leave the country an re apply for student visa overseas. Im planing on going to HK, how long does it take to get a visa in HK? Thanks