You cannot redirect away from the survey and then return to the survey unless using token response persistence, and this will return you to the last
submitted group, not the last group you actually saw.
A couple of alternatives...
1) Two surveys, the first survey redirects to the remote website, that website then redirects to the second survey. You can prefill questions in the second survey via URL parameters -
manual.limesurvey.org/URL_fields#Prefill...using_GET_parameters
2) Place the remote site in an iframe and pass actions up to the parent frame (the survey) via JavaScript messages -
developer.mozilla.org/en-US/docs/Web/API/Window/postMessage
In either case, you will need some access for coding on the remote site.