I wanted to do this as well. My employer uses HealthEquity HSA and I have a Fidelity HSA. I did a one time transfer imitated from Fidelity. Unfortunately HealthEquity messed it up and ended up transferring everything and closing my account. It was a pain trying to get it opened back up so that my paycheck contributions could continue.

Anyway, you can do it without any tax penalty. The safest way is to go online to Fidelity and ask them to initiate the transfer. You can in theory do that as often as you wish