Yes the ********* MICROAMP HA400 Headphone Amplifier will work with your AudioBox 44VSL.
You will need to set up a Bus or Aux track in your DAW and route the output of that Bus/Aux to Outputs 3/4 of your AudioBox 44VSL.
You can then connect Outputs 3/4 of your AudioBox 44VSL to the Stereo Input of your headphone amp. You will need a stereo to 2 x mono 1/4 inch jack cable to connect, such as the one in the link below.
https://www.thomann.de/ie/the_sssnake_ypp2010.htm
Send the signal from your respective channels in your daw to the Bus/Aux you created and you should be good to go.