How would I use a search engine from another site in a form

I’m not sure if this is even possible or not, but I help run a Pennsylvania political educational site and something we’re lacking currently that would very helpful for our viewers is the ability to search for their legislators. the main state site allows for this, but I’d prefer to have an option for this on my site and then I suppose use their system to produce the results if that’s even possible.

the site I help manage is on the joomla platform and here’s the link to PA general assembly site-

is this possible with a form?!

If you copy all their form parameters you can use a form from your own site to submit to their site.