Or am I totally confused and you are not saying Smokefree is an 808?
And which battery do you want to use with what? "the battery" is unclear.
..........
Ok - I think I found it. What ripoff. OMG $55 for an atomizer that should cost $7. $55 for a battery that should cost $12.
IF <- important! IF the battery is greater than 9mm diameter (not less) AND the bridge does NOT poke up out of the atomizer then I think it is probably RN4081. If it is greater than 9mm diameter AND the atomizer bridge does poke out of the top of atomizer tube then it MAY be DSE103 which would use the same adapter as RN4081.
buy a 4081 to 510 adapter from Goodprophets, Madvapes or Altsmoke and try it. If that works then
buy the other adapter too, Or you could
buy them both at once if you want. They may or may not work. (Somebody else had a similar model and it ended up being neither RN4081 nor DSE103 but looked so much alike. We never ID'd that other one - was just some Chinese rebrander model made to look like RN4081 but hopefully yours actually is.)
IF the diameter of the battery under 9mm then it is some Chinese wholesaler model and there is no adapter available for it