Some Passe Passe Bottles have a valve so that the glass below can be refilled. It opens when pushing a plunger in the bottleneck.

One bottle I have has a problem. I can push the plunger but the valve does not open. The little rubber cone is loose on the plunger, the washer below seems to have never been fastened to that rod. So the rubber cone sticks in the hole, the plunger operates only the rod without any effect.

Does anyone have a solution to that problem?

My guesses are:
1. Cutting out the double bottom, removing the valve and later glueing the bottom back in.
2. Trying to glue the washer and the rubber cone with some glue while the valve is still in the bottle.

Has anybody ever built such a valve himself and knows a more reliable version for DIY?

I added one to a bottle years ago. Remove the old plunger, if you can. See if the parts can be salvaged. If not, you know the basic premise. You need a rubber stopper that will fit the hole. You need a threaded rod, plus sufficient washers and hex nut. Since you can more easily work through the bottom, you will build from the top, down.

In other words you will partially assemble the rod, insert it down from the top (neck), and then finish the bottom end (where the stopper will be).

The rod must have a stop, so that when pushed down to release the stopper from the hole, the entire unit doesn't fall out the bottom. This can be as simple as a washer secured with a hex nut on each side to lock it in place. The washer would be larger than the hole, of course. You can also solder this washer in place, too. It's proximity would depend on the depth of the upper liquid chamber. You will need to add some type of handle, or terminal to the top of the rod. This is what your finger will actually contact.

If you have a hex nut that will fit through the hole, add it to the bottom at a height where the top of the rubber stopper will be. If you can solder this, all the better.

Once that much is assembled, feed it down through the neck from the top and through the hole. It will go down only so far before the washer stops at the hole.

Now, from the bottom, add the rubber stopper to the rod and snug it up against the hex nut (you can add another washer in between if desired, as long as it is smaller than the hole).

Secure this in place with another washer and hex nut. A socket wrench with a long extension will make this job a snap.

Push the stopper up from the bottom until it jams in the hole. Your upper compartment is now water-tight. Fill the upper compartment with enough liquid to properly fill whatever glass will be below. A finger inserted into the neck can push down of the rod, dislodging the stopper, and allowing the liquid to drain down through the hole into the waiting glass below.

Of course what you really want to do, is fill the compartment with twice as much liquid as needed to fill one glass. Then, in the course of the routine, pour from the bottle to fill the visible glass. You will use half of the liquid reserve. The plunger then can be used to fill the hidden glass before revealing the Passe-Passe effect.

The info given is a basic idea. You can embellish the mechanics to make them operate more smoothly or quietly.