Connect two screens with a single HDMI port

"impossible to find a solution to connect the two screens at the same time but with different images".

It is indeed impossible. An HDMI output can only display one image at a time. It is possible to show the same image on two screens, but not two different images at the same time.

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Misnaming things adds to the misery of the world (Albert Camus)

I know that, but could there be a solution through perhaps an adapter that could serve as a second HDMI?

Not exactly, I found an adapter that connects DisplayPort to HDMI, and I would like to use it to capture a second screen, meaning having a second display but with a different image (extended screen). I hope I was clear. I don't know if this kind of product will work.. https://www.amazon.fr/gp/product/B010SDZZ80/ref=ask_ql_qh_dp_hza

Hello
instead of (censored)
specify what PC you have, or which graphics card
each graphics card has several ports: vga, hdmi, dvi, DP
from there, you can set up 4 screens through duplication or extension

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