How to programmatically fill in a form if it is not originally on the page?

Question

PHP

I am searching for books in Moscow libraries. I programmed a search in the Business Library, now I need to do it in the Consolidated Catalog (SKBM) . If anything, it does not include some important libraries, such as Delovaya, for young people, so the project makes sense.
I need to programmatically fill in three POST parameters: in the select, the item "Title", the title of the book and the button.

I learned how to work with the POST method through Guzzle, but the SKBM form is not simple: there is no select tag, no name attribute for the field and button.

What parameters should be sent to the issuance page ? Help me please.