Can iOS-devices take sound in and send to Airplay?
I found a solution. It is described in detail below.
What you need

a RIAA preamp with USB Audio output, such as a Behringer UFO202
Apple's Lightning to USB 3 Camera Adapter
an iOS device with GarageBand installed

The steps you need to follow

Connect your record player to the RIAA preamp

Connect the RIAA preamp to the camera adapter.

Connect a Lightning USB cable to the camera adapter (unless you want to run this on battery power).

In GarageBand (on your iOS device), select Audio Recorder as the instrument (see screenshot below taken from an iPad):




Turn on monitoring



Select Stereo as the Channel and enable the Monitor option (see screenshot below)



OPTIONAL: It may be a good idea to increase the Out volume (use the vertical slider on the right)



Switch on your record player

Set your iOS device to use Airplay speakers for sound playback


Now, everytime you want to use your record player you can just connect your iOS device to the RIAA preamp and it'll become an input selector.
NOTE: If you get a warning about delays and latency you can just dismiss it.