Can I fix an inner tube if the valve has been pushed inside?

If it’s simply that your inner tube valve pushed in, then you most likely don’t need a new tube. You can just partially pull back the tire where the valve opening is and stick the valve back through. If you’re lucky, you might even be able to do this without peeling the tube back. It just takes some massaging - it helps if you have experience being a midwife or animal husbandry.

That said, it’s always good to have a spare tube. When the valve gets sucked in like that, it often gets crimped at the valve base and leaks and that can’t get patched easily. Inner tubes are cheap so it’s good to always have a backup.

Especially with presta valves, it’s good to use the locknut provided. Don’t tighten it too much (especially when the tire is inflated) or it’ll be very hard to take off with bare hands when you get a flat. But that locknut is designed to prevent the valve falling into the rim well.

Thanks for the photo! This makes it clearer that your valve body didn’t fall into the wheel rim, rather your presta valve internal valve shaft either fell off or fell into the tube body.

Unlike the photo above, it looks like you have a one piece valve so the core isn’t normally removable (you can’t unscrew the part of the valve pictured above with the words unscrew here) — but if you were to unscrew the thumbscrew too far the inner valve shaft itself could fall into the inside of the tube.

You’ll need a new thumbscrew at minimum but it might be very hard to get the thin internal valve shaft back up into the valve body properly. Unlike a tube with a replaceable core, I don’t think you can replace the core if you can’t rethread the valve shaft from inside.

In many ways, it’ll be easier to just replace the whole inner. They are cheap for a reason.

If this ever occurs, make sure to remove the inner tube out of the tire and wheel. Next, locate the inner shale valve (long copper screw) by touching the inner tube and feeling where it is. After, reinsert it into the main body. Finally, it may be difficult at first to locate and attempt to insert it however if I can do it so can you! Don’t waste your money on buying a new inner tube. This issue can be fix within minutes. Thank you!