Building a circuit to replicate a LiPo battery
I'll put a formal answer on here, maybe it helps, maybe it doesn't. This isn't a way to simulate your battery, but it is a way to keep your phone plugged in and alive for a long period of time. A decent smartphone battery with proper charge cycles should last 2-3 years.

I personally don't like the idea of opening up smartphones. I generally don't like opening up any consumer hardware, because unless it is already broken, I usually break it. Additionally, you're never getting datasheets or schematics for that phone so any tinkering is all best guess.

My solution around this is to simulate the charge cycles.


Easy method: a simple timer. One that plugs into a wall socket. Once your phone is fully charged move it over to the timer then the timer turns back on in roughly 12 hours. That time would need calibrating but this is a very crude setup that would extend the life of your phone. Your comment that this would drift and we wouldn't know how long it is not charging for is correct. I don't know what kind of battery life drain we would see in six months. This may not work if the phone won't be monitored for six months.
Hard method: A more sophisticated way could be by using the power of IoT. Using an app like Tasker (maybe?) or even writing your own app, you could monitor the battery life of your phone. Once the battery gets too low the app-in-question could send out an email or an SMS. The email or SMS gets picked up by a service like IFTTT which then sends a command over the network to a smart plug for your home. This solution would have your phone always start charging at the exact same percentage and stop at the same high-level. It would also require much more setup and the internet.
The same as above, just not as nifty: you download a battery alert app -- one that plays a loud sound when the battery is low. Build a small relay circuit with a microphone. When the sound goes off, the relay closes. Maybe it can play another sound when it's full as well.


My point here is that there are probably a dozen more ways in which you can extend the life of your phone. Hacking the battery charge circuit is one of them but consider some alternatives. If simulating the circuit is really what you need then don't accept this answer. Someone else may have more of an idea about what your smartphone is looking for with its battery connections.