Dual USB-C and USB-A dock

[Ben80]

Hello,

I have the HP Universal dock USB-C/A G2 that I use with my professional laptop (HP 840 G5 with USB-C connector) and my personal laptop (Macbook air 2015 with USB-A adaptator). It works fine.
However, this dock doesn't work with my Samsung S20 with DEX. I connected it to my dock with USB-C and my dock is linked to my HP monitor with HDMI but my monitor doesn't recognise the signal.

I can mirror my S20 screen with Displaylink Desktop for android but can't launch DEX.

According to the HP notice, the USB-C connector use DisplayPort Alt Mode.
Could you please help me to connect my Samsung S20 with DEX to my HP USB-C/A G2 ?

For your information, one of my colleague use a Dell dock with a similar system (DELL D6000) and have success with DEX.

Thank you for your assistance.