Tell me, please, how to translate the first letter of the string to the lower case in Cyrillic?

Answer 1, Authority 100%

Separate the first character from the rest of the text and give to the bottom register, then attach it back.

$ value = 'Born on the street Herzen, in the grocery number twenty two.';
$ Value. = 'Famous economist, by calling your own - librarian.';
$ firstchar = mb_substr ($ value, 0, 1);
$ firstchar = MB_STRTOLOWER ($ firstchar);
$ otherchars = MB_Substr (
  $ value
  1,
  MB_STRLEN ($ Value)
);
$ Value = $ Firstchar. $ Otherchars;

more stylish option in the form of a function, use on health.

Function FirstchartolowerCase (String $ Value): String
{
  $ firstchar = mb_substr ($ value, 0, 1);
  $ firstchar = MB_STRTOLOWER ($ firstchar);
  $ otherchars = MB_Substr (
    $ value
    1,
    MB_STRLEN ($ Value)
  );
  Return $ Firstchar. $ Otherchars;
}