The phone as shown on the photograph is a German-made, postwar model W49 (Wählfernsprecher 49, post office nomenclature) which was an extraordinary developement of a desktop phone that could be converted to a wall-mounted by only losening a few screws and rotating the dial mechanism and hook-mount. EZ2-Convert, as some would say. Entering "W49" and "Schaltplan" or "Stromlaufplan" in any search engine should produce satisfying results as to the circuit diagram.
The capacitator doesn't serve any oscillating purpose here and party-lines were (and still are for legal reasons) uncommon in Germany. I don't know any specifics about foreign (e. g. english, french or american) phone systems, but I guess they were all based on the same principles so there weren't any essential differences, and the german phone system operated with ca. 60 VAC/25 Hz ringer current (Some went up to almost 120 VAC, so tampering with the line could sometimes very well result in quite painful, in any way dangerous experiences...). As the receiver was hung up, the hook switch disconnected the phone circuit but connected the ringer circuit to the line. In order to block the DC current and as such keep the line-finder switch at the switch station available (The line-finder was the first step in the automatic switch station and replaced the human operator, who answered "Hier Amt, was wird gewünscht?/Operator, what is requested?" There weren't as many line-finders as there were subscribers. The post office relied upon not every subscriber requesting a line at the same time to keep cost low.), the capacitator is needed. It charged itself on the DC current which thus couldn't pass. As now someone called that subscriber number, the switch-station applies ca. 60 VAC/25 Hz on the line and that AC current "didn't mind" the capacitator and so the ringer struck the two well-aligned metal bells to produce the clear and high beating ring. Of course, all this is now history as VOIP took over that merely emulates analog telephone lines.
So if you'd like to make a DIY-Ringer, all you need to take from this phone is the ringer mechanism itself that consists of the two coils in the middle and the mount that also holds a permanent magnet and the clapper. First, you need to remove the hook-switch that is mounted above the ringer. There are two screws clearly visible and easily accessible (in fact, apart from the mounting screws of the bells, these are the most prominent screws on the photograph...). Probably the same screws also hold the ringer coils on the base plate, so maybe both come lose now. If so, just clip the wires and you'll have your ringer coils. If you'd like to have the original (and if properly adjusted, also quite pleasent) sound, you might want to take the two bells, too. The bells are mounted excentrically just a bit so proper adjusted clappers just won't touch the bells if you moved it by your hands. When AC is applied and the coils become excited, the clapper will have enough momentum to reach the bells, just find that sweet spot. Be careful, however, not to losen any adjusting screws, as the clapper's anchor must be properly adjusted in relation to the coils. I don't know the proper english technical terms, but the german terms could be translated as pole-shoe (at the coil) and sticking-nipple (at the anchor) should not be more than 0,5 mm apart if the clapper sticks to the opposite pole-shoe.
If you are in possession of the bakelite housing, however, I'd strongly recommend not to cannibalise any of the electric parts and to keep the phone as is, since these weren't as wide-spread as the more common desktop phones W28/48. Your phone is complete as to the electric part and seems to be in the original state, the capacitator sports a "checked"-stamp (you may barely read it, but the part of "geprüft" is visible...) but that's it. Maybe the phone wasn't as beaten up as many other W49 which were mostly used in rough conditions at workshops (where wall phones would be the norm). Not many survived because the concept of a convertible phone didn't succed for the simple reason that telephones became more affordable and instead requesting the post office to convert the phone (No subscriber was ever allowed to do anything to the phone, of course.), an additional phone was installed and that was that. These phones were refurbished until end of useful life and then could be purchased by post office members for a few Marks to be used in private installations only; sadly, most went straight into the bin. The desktop brother W48 is in fact still in production (small numbers of course) and may be bought for quite high a price.
