I’ve tried AX and BG; neither fit; I bought this light years ago; does it have different threads?
How about the short tube of an S41?
I had one of the first series A6. The short tube of the S41 fitted.
But the (long) tube of the A6 did not fit the S41.
The interchangeability of parts of the same model “manufactured” by BG is a lottery… especially in the best-selling models.
I do not know if it is because the batches are ordered from different factories or because the tolerance of the measurements between batches is very large.
I would say they have had different threads along the way.
Recently I tried to make a shorty Convoy S6, with an astrolux 18350 tube and it didn’t fit, while I’ve seen similar builings in the past with such tube. Sad thing 
the a6 also has an annoying tube feature
the tubes have same thread size on each end
but they only go one one way
one end is longer than the other—by about 2 mm
if you install wrong, the light will not work, though it does screw together and looks like it would work
that may vary as well, i don;t know
just a quirk i noticed