Oh, my apologies; I misunderstood. It got loose from the outside dual and popped through so it's on the backside of the outside dual between the two wheels?
Maybe try screwing the extension off so it's not attached to the inside dual valve stem and once it's off, pull the extension toward you until you can pull it through the stabilizer/grommet so it falls to the ground.
You then should be able to screw the extension back into the inside dual valve stem and slide the stabilizer/grommet over and through the the extension so you can push grommet into place by following the advice others gave you by using a screwdriver or soapy water, etc. to push and maneuver it into place from the outside. I can usually massage and wiggle it into place by hand but you can use a screwdriver or soapy water if you see the need.
I hope that makes sense or works in your case but I'm awful at trying to describe how to do things.
ETA: These videos may help to picture in your mind what I'm trying to describe even though they aren't addressing your exact problem ...in the second video, at about :40 you can see her screwing the extension into the valve stem of the inside dual. That's what you would do once you unscrew it to get it off the grommet/stabilizer so you can insert the grommet from the outside as she illustrates in the video: