The cylinder appears to be one of the older 6351 alloy tanks that have a requirement for Eddy current testing of the neck threads for cracks due to sustained load cracking. No scuba store I know of will fill them and during my occasional employment in such stores I will NOT fill them, period. And many scuba stores will not fill aluminum cylinder that are older than 15 years because they do not want to. Luxfer long ago gave an incentive to purchase new tanks not of the 6351 alloy.
A new 80 cf aluminum cylinder can be gotten on sale for under $200 (Diver Direct, $169.50, Catalina 80) with a fresh hydro and the scuba store required VIP inspection. Nobody is going to do the expensive eddy current inspection on an ancient 6351 scuba tank. It is worth it's weight in scrap and no more. And even if it had the eddy current inspection it is unlikely a store would fill it or VIP it. Because they do not want to, their store, their rules.
If by checking the first hydro date it is a newer cylinder and not involved in the Eddy Current requirement, have at it. Again, many stores will not fill a cylinder over 15 years old even with current hydro. Some will, many will not.