Thank You tolik25251!
It seems that this patch works. Persons at least now showing correctly. I'll watch what will happen in other sections.
Once again, thank you very much, tolik25251 You're the best!

Tolik25251 or someone, are you can explain more in details how to change encoding to UTF-8.
I have changed:

1. All ISO-8859-15 charsets in Theme files to UTF-8 and also "de" to my national
2. Encoding parameter in config.inc.php to UTF-8
3. And line 128 in functions.inc.php to "function isys_glob_prepare_ajax_request($p_charset="utf-8") {"
   … but still have problems with national characters. When populating tree object or data in display-form names displayed normally, but when I press edit, they are displayed incorrectly.

Thank you in advance,
Dainis