The request is reset when moving to another page getPage

I ask for help in solving this issue ... The essence of this ... I deduce from my database table a list of elements on the page using getPage. The request data is passed to the snippet using the POST method from the form. And everything is displayed correctly, but ... just before I turn to another page. Request data is reset. That is, if I was looking for a person by the name of "Ivanov", then when I switch from the first page to another, I’m already showing all the people in a row. Is it possible to somehow save the request data when moving to other pages? Tell me please. Or share the link. I don’t know anything. Thank you very much in advance.