Add a drop of superglue in the bottom of the center hole and then add the cap to the rod and insert that into the center hole. Don't press it too hard or else the glue might push up onto the cap or the cap might be difficult to turn.
I made this to fit inside a standard 16 dram pill bottle, like you would get from a pharmacy, to help contain the smell and find another use for old bottles.
The last version that I printed was a bit too big for the pill bottle so I made it a bit smaller. It should fit now but I haven't printed it to check.
Printed on BambuLab P1P at 0.15mm layer height
onshape link: https://cad.onshape.com/documents/59dc3adcdf67bbeda788f0e8/w/a7110bf9e544d67c0e4056b6/e/af24a7d530c2c0f5954fbc3b?renderMode=0&uiState=6540301667c786101a2b706b
The author marked this model as their own original creation.