1) I downloaded all data from my MySQL DB and FTP
2) because of bad encoding in my database (wrong collation) I replaced all incorrect diacritic characters to make sure that the data would show correctly on my forum
3) I changed MySQL settings in config.php
4) I imported the database to another MySQL server (I did the same with downloaded files from FTP)
5) I changed the IP address of my old web host to new IP address in my domain's DNS settings
When DNS of my domain has been updated, I visited my forum. There was shown
this page.
6) I changed my DNS record back to the old value