Connect Playstation with projector and surround system?

I have a question about my home theater which I'm setting up.

I would really like to watch films and videos via the projector with my playstation, but get the sound via my surround system.

the problem is: the amplifier unfortunately has no HDMI in and out, which is why I can't get any sound.

is there a way to get surround sound?

The PS4 also has an optical output (Toslink), which your receiver should also have. To determine this, the exact model name would be important.

That means, I connect the PlayStation to the projector via hdmi and to the amplifier via optical cable.

I checked and my amplifier has the necessary connection