Load Contents from Website B and Put on Website A

I have a website built in Laravel but the catch is, I cannot give access to chnage anything on it. I am a somewhat experienced developer but needing help. I can let you view through teamviewer. So I have a website(Website A) that I want to implement eleemnts that another website on the same server (Website B) loads. Website B has a search button on the main page where which you enter a serial # and then it loads the data for that serial # upond pressing search. I need website A to be able to have its own search button, which when I click, it submits to Website B's search button and then returns websites B's data that it loads after searching. I want the data that website B loads to be on Website A in my own ways of styling(I want to be able to target specific elements from website B. Please let me know if you have any questions. This will be done though TeamViewer