found a solution by myself^^ maybe it helps other people with the same problem:

i used the developer module, went to forms/persons search/ and clicked there on "reset" - path of url is this: studio/module.php?name=bx_developer&page=forms&form_page=search_fields&form_module=bx_persons&form_form=bx_persons

after that, the search field, which i have added before are available. i do not know, if this is the normal way to do that, or it is a bug, of course it is very uncomfortable.

you should know, when you click on "reset", all settings are away, so you must set up all again for the person search. best way is, first add all search fields what you want and then click on reset, if the fields are not added automatic to persons search

with una script, it becomes never boring.... =)