good morning
for your question i have a a book (crown jewels :the mauser in Sweden).in this book
at page 148 ther are the list of S.N: Your serial number is in middle betwen 371495 and 401598 .the year is the 1916.
i have no trace for the hh but i suppose is the inspector control in 1916.but are you sure is HH and no HK?
i have a cg m41/b (sniper) and serial number is correct for the year
bye Pasquale
P.s. sorry for my English
my email is pasqualedes@aliceposta.it