Submit a Search Button From an External Page and Return Its Results On My Own [Same Server]

I have a website built in Laravel but the catch is, I cannot give access to it. I will need to be instructed on how to do this. I am a somewhat experienced developer but needing help. So I have a website that loads up basically a search button to search a database and return some results depending on what was inputted to the search box. I am wanting to execute this search from an external page and receive the results from the search so that I may style them myself on the page. This is not cross site, both of these websites are on the same server IP. I just need to be able to basically put a search and submit button on page 'A' that will execute the search and submit button on page 'B'. I want all of the results from page 'B' to be displayed on page 'A' so that I can style them however I want. If you have any questions then let me know. This should be a fairly simple task. Remember though, I cannot give access to the server. I will need you to tell me what to out and where. I'm not new to development so no worries about confusing me. Thanks