Is their a possibility to let a user post on the forum but make the posts he makes only visible to himself and not to other users / guests? I am aware this is a strange question but it's a strange situation and I'm afraid this is the only possibilty at the moment.

Thanks in advance!

Yes, it’s a per-forum settings. 

(But admin will always be able to see anything.)

On 3/13/2019 at 5:39 PM, opentype said:

Yes, it’s a per-forum settings. 

(But admin will always be able to see anything.)

Can you advice me how to do this? 

Turn that off in the settings for the specific forum:

But that would apply (as @opentype mentioned) to the entire forum, not just a singular user.

Could this be done with a member group?

You seem to want that “silent member” feature. There are a few topics about it. That will make the user to create another account, etc.

Oh right, I misunderstood the request.

No, don’t do this. It is a terrible idea and very unlikely the “only possibility”. 

Could you leave it so that they can post but everything needs to be approved so it would be automatically hidden; staff could still see, the member could see their posts - but no other members could