How to power a phone with no battery properly?
In theory, I don't see why applying the specified battery voltage on the correct battery terminals would not work. Try to avoid overvoltages!

Obvious reasons are not obvious to everybody. I assume you don't want the battery in the loop so you don't have to worry about it aging over time, bloating and potentially causing problems?

A linear voltage regulator would probably do the trick. I would personally add a good amount of capacitance between the regulator and the phone to smooth out any sudden changes in your phone's power consumption. If you want to ensure you never go over a safe voltage, a Zener diode would be your friend.

Good luck, and let us know of the outcome!