Yes. Pre-existing HSA funds or MSA monies may be rolled into an HSA and will continue their tax-free status.
Starship can make this easy for ya.
Tap on Profile in the upper right corner
Scroll down and tap HSA transfer
Transfers can take 4-6 weeks to fully process and transfer over. You can log into your account anytime to see what stage your transfer is currently in.
**Transit times vary based on the origin bank**