Can I transfer my company stocks from UBS account to Fidelity?

I am employed by big company. Was awarded company stocks during my employment. Those were awarded and being handled by UBS. So right now I have special account at UBS that was created for me by my company where all those stocks are. It looks like it is limited in what I can do there - I just have option to keep the stocks on sell them for cash. I want to diversify and change part of the stocks to some ETF. I already have an account with Fidelity. I there any reason anyway to transfer then to Fidelity and purchase ETF ? I am a beginner, so excuse if the question in wrong