If, the act of removing that phillips screw will release the battery and allow the battery to slide out from its enclosure then we have only solved part of the problem.
Does anyone know if/how the remaining top part of the case could be pried off of the hearing aid electronics? These was some discussion here, How to replace hearing aid housing.
In most disposable battery types the circuit board just clips into place, so this is probably the same,but I don’t think you would need to remove the circuit to replace the battery, I don’t think the wire connecting the battery is going to be the end all, finding a way to remove without to much damage is the key, the battery size could be hard to find tho.
As for working with things this small, jewellers tools, anti-static mat and a USB microscope like these
https://www.amazon.com/USB-Microscopes/b?ie=UTF8&node=2742273011
Thanks for the tip about Digital Microscopes. I was unaware of that technology.
I don’t follow your vision about battery removal with the case blocking the path for removal? The battery would need to slide out of the battery enclosure in the direction indicated by the arrow, right? It seems clear to me that the case is blocking that particular battery removal path?
Also; from @sterei 's pictures there will be two wires;
Yes, actually looking at that again does seem you may need to do that, yeah 2 wires for positive and negative, I’m interested enough to try it with the Unitron models I have (Marvel equivalent) as I’m quite sure they’ll be the same under the skin.
Have been using a jewlers loop to view the screw, even took an imprint using bluetac and its a 4 pointed (Philips) screw
Wires are connected to the battery directly (most likely welded as previously discussed on this thread) so not an easy way of removing and replacing (needs the right equipment)
I am so grateful to find your post. Thanks.
I have Phonak Audeo Paradise P90R’s which are rechargeable. Every bit of knowledge helps.
I found other naked pictures of a Phonak Audeo Paradise P90-R hearing aid. It seems that Phonak’s technique for attaching the wire to the battery has changed/evolved. So I replaced the pictures in the DIY School PDF file named (05 Buying Rechargeable Hearing Aids). Meanwhile, thanks to @Vigilo for the temporary use of your pictures.
Varta has a new line of Li-ion rechargeable button cells!
Their contact form even allows you to specify hearing aids as application. They also ask the number of cells required annually, though, so it is not meant for consumers.
Looking at the documents on the linked page, I constructed the Varta coinpower A4 code to be CP7954. However, Google generated no hits. Close to it is the CP1254 on Conrad. However, that one is 12mm wide with 74mAh.
Back to the data sheets there is a CP7840 F1 with 12.2 mAh. The previous generation button cell, the Varta CP7840 A3, has only 16mAh. So that road seems a dead end.
Looks like that either Varta won’t be helping us with this generation or that the mAh needed for a HA is much lower than the 55mAh, that I estimated (rather roughly) in a previous post. Looking at the rechargeable PowerOne 13 cells that capacity is 28mAh, so both CP7840 seem to weak.
Maybe these new Varta button cells are too weak. But they surely have a pretty picture! Congrats to the professional photographer who produced that picture! 
btw> I would like to link to the other thread where there is ongoing attempts to replace these built-in batteries. Here’s a link;
Insight into the inside of the hearing aid
