I know some people say that the 390AMX was available in 1977, but there are no identification numbers listed in ANY published or otherwise literature to support this. Maybe you can find a magazine test in late '77 but I believe it will be a test of the '78 model. The earliest listed is 1978 390AMX with an engine prefix of 2070. 1978 model Husky's are generally not accepted as pre '78 legal bikes although the 3 major differences, 1: tapered steering head bearings,2: slightly different swing arm (no reinforcement plates on front cross section), & 3: slightly different rear hub, in my opinion hardly make them vastly improved over the '77 model. The '77 390 manual engine (2061) ran till 1979 unchanged & the 1978 CR125 uses the '77 chassis (all capacities), same part number, but will have a 1978 series frame number. The 125 engine ran from 1976 t0 1981.
Another can of worms if you want to run a 390AMX in pre '78 where it belongs.
Oh, by the way you'll still have to restrict the standard 1977/78 suspension travel to comply with the pre '78 rules as well. Don't understand that one myself but them's the rules.
K