Powering while charging

Hello fellow arduinonauts! XD

I have been working on a project that runs off of a small rechargeable lipo battery (150MaH).

HOWEVER.

The battery is not removable and is soldered as well as glued into the circuit, and is charged via a magnetic connector.

I would like to be able to use the device even when it is charging... so the question.

Is it possible to charge the lipo battery, and power the circuit at the sametime off of the same power source,
and if so, how would I go about doing this.

Any sort of information, schematics, or links would be greatly appreciated!

This product page includes schematics: