Long Branch MK I* qeustion

[Sunray]

A 1941 Long Branch '*' receiver is very early. That's when the "conversion" to the Mk I* began.
However, that one was likely cobbled together out of parts bins with zero QC. The CAI ST A B VT stamped on the muzzle is Century Arms International, St. Albans, Vermont. It's not an import stamp. They are well known for assembling Lee-Enfields by the thousands straight out of parts bins and no QC to ensure they were safe to shoot.
Really only means you must check the headspace before even thinking about shooting it. So do not shoot it again until you have done so.
You can buy headspace gauges from Pacific Tool and Gauge or rent 'em from Reamer Rentals(this is the least expensive).
It was possibly refinished and likely stocked at the same time. The "303 Can." is them too. Neither the rifle nor ammunition was ever called anything buy .303 British by anybody else.