How can you get your phone to work without a battery?

It can't work without power.

(alternate answer) In principle there are a variety of ways to provide a phone with electric power. Of course, the simplest alternative to a battery is to use a land-line which draws current from the wall (I still use one, myself). For a mobile or cell phone, there are other options. You could use a solar power panel (I own a calculator that runs on a small solar panel; calculators don't use a lot of power, they use much less than phones do) or a muscle powered generator that you crank by hand (there exist radiOS that work by means of a crank). However, if your phone is not built to work that way, it will be difficult to retrofit it to work differently. Tell Apple that you want them to make a solar powered phone for you. But remember, solar power has its limits. You get no solar power at night, for example. A hybrid system, which still uses a battery but which recharges the battery by means of solar power, is more practical.