Opening popup on another companies website - possible?


I have a wierd problem and although I am not a programmer I’d like to
know it this was even possible.

I have businesses that send me email addresses of people referred to
them by their customers. They also have a picture of their customers on

I would like to send an email to the referrals that includes a like.
When the referral clicks on the like a browser opens on the businesses
website and a popup window opens that contains the picture of the
custoomer (ie. the person that referred them to the business).

I will send many emails and each will include a different picture and
potentialy open a browser on a different businesses website.

I cannot make any modifications to the businesses website.

It is possible to write an application that does this.