Glad you were smart and had your mom get out of that trial!
If the male threads are on the cartomizer than it is probably an RN4081 but there are some smaller combinations with male-threaded cartos that rebranders use so if the diameter is the same as a cigarette then it is probably not RN4081. If the diameter is about 9.2mm then that is how thick RN4081 is. If it is Rn4081 then you can also use the Njoy Npro or Njoy 2-n-1 cartomizers some 7-11s sell.
Try some blank RN4081 cartomizers. Rebranders lie about how long carts and batteries last. A cartomizer does not last as long as a pack of cigs, and certainly not if you want to refill it and use it for longer (in which case you should not run it dry and should add
juice and keep it wet inside). I love cartomizers but you do have to refill them.
Order some nice ejuices. Try ones that are PG/Vg blends because that way you will avoid the Chinese 100% PG and 100% VG juices. I like Backwoods Brew, FreedomSMokeUSA (I get 70pg/30vg when offered), Velvet Vapors (I get their Velvet Blend PG/VG)
I don't know if RN4081's are the easiest to fill. I've mostly seen videos where they seemed to using methods that implied the caps were glued on (like using a cover off a tiny paintbrush as a funnel to get the juice in). But they may have been refilling the some from a rebrander that had glued-on or hard caps (rebranders like to try to keep customers from refilling)
Search Youtube for: fill 4081 cartomizer
That will bring up several videos - hopefully one will be useful for the cartos you have which you look for more.
AzSmokeFree has some RN4081 cartomizers (battery+cartomizer is 2 piece ecig) and also sells an RN4081 atomizer and RN4081 carts (battery + atomizer + cart is 3-piece ecig) - RN4081 can be either
Vaporkings.com also has RN4081 stuff including blank cartomizers
So if you think what you have is RN4081, then search either site for RN4081 to find parts etc