Can someone suggest / point me some simple and tested php script to put of all files on remote web server in one tar.gz file for easy download / backup?

Why use PHP for this? Why not some scheduled task (whether it be batch of PowerShell for Windows or some CRON job or PERL script or something)?

EDIT: Am I right in guessing that you are using a Linux or Unix server being as you want to output to tar.gz files?

I do not own this server and I'm not an expert in this. All I know is that my page is located on remote FTP server, this server is able to run php and create tar.gz files. I do not need scheduled and frequent backups - just from time to time, on my command.

Actually I've noticed I could create *.gz files, not sure about *.tar.gz (if it makes difference).

After googling a lot I've found solution suitable for me I think.

Case closed.

tag it as solved then

I cant, because I can't mark my post as solution and I've found solution myself.

Since you found the solution yourself it's irrelevant which post you mark as solved, and the reason why users can't mark their own answers as solved should be obvious. You can close the thread though by picking the the most useful answer. In this case is not really a big deal since it won't carry over to the support pages, but still...

...or people could just let the thread fall down, and eventually out of, the first page by itself. It's not like every thread marked as a question absolutely and desperately needs to have a post marked as the answer.

If every thread marked as a question absolutely and desperately needed to have a post marked as the answer i wouldn't have said that "in this case is not really a big deal", no?

The only reason i bothered was because i thought that maybe Lexor was unaware that there's a reason why users can't mark their own posts.

But people went through at least a little trouble to try help you solve your problem, so the courteous thing to do is to at least give a nod to the best attempt.