Rick, I found some Swedish information which may help.
Vapen-Depoten AB in Falun was a Swedish gun, hunting and fishing dealer, so the name on the gun does not necessarily identify the maker.
There is actually a Swedish discussion specifically about a double gun marked "Vapendepoten" and "Special". The author was also looking for catalogue information on this model:

http://forum.robsoft.nu/viewtopic.php?t=266076

There is another Swedish discussion concerning Belgian shotguns sold by Vapen-Depoten in Falun:

http://forum.robsoft.nu/viewtopic.php?t=26117

A complete Vapen-Depoten Falun catalogue from 1969, No. 105, has also been digitized and can be seen here:

https://archive.org/details/vapen-depoten-falun-1969

There are also earlier Vapen-Depoten catalogues known, including No. 81 from 1945 and No. 83 from 1947:

http://forum.robsoft.se/viewtopic.php?t=164795

So I think "Vapen-Depoten Falun Special Export" is probably a retailer/importer or model marking rather than the actual maker's name. If your proof marks are Belgian, Liège manufacture would certainly make sense.
Pictures of the barrel flats and action flats might tell us more about the actual maker.

http://www.hunting-heritage.com