By authentic do you mean similar look to what it originally came with or an actual original strap from how it was sold? I feel like your search may be fruitless on that end, unless you find a NOS 44GS somehow.
Box may be easier to source using Yahoo Japan auctions with some patience.
Anyways, not much help, but lovely watch! I think it looks pretty good already on its current strap.
I am looking for an authentic band for my 44GS. I also would love a box but not sure where to start looking for either. Any help for a newbie?