PTM - I believe that Fidelity changed their law and you can transfer now ..
March 12 this year I went in person to Fidelity office to open account there and deposit certificate I had for no restricted shares from our company ..

First they told me that they can only accept restricted and they will not be trading ..

Fortunately I knew someone who recently deposited shares and he knew that their law changed .,After he explained to them , they checked again , and did accept my shares ..

So I will advise to speak with them , just know that law changed there recently , not everyone may know , so they need to check well , and they should accept your transfer .