I have a question regarding the following context:

People click on an advertisement (eg. facebook Ad) and are redirected to a specific website (Website A). By clicking on the advertisement, the link is enriched with utm_campaign, utm_medium and utm_source-Parameters. On this Website (Website A) there are several buttons (let's say Button A, Button B, Button C), which all redirect a visitor to a new Website (Website B).

What I want is that, depending on which button is clicked, the url with all the tracking parameters from the advertisement should get enriched with additional parameters that are contained in the link of the button.

Let's make an example to clarify:

1. A user clicks on an facebook-Ad and is redirected to websiteA.com?utm_source=facebook&utm_medium=paid&utm_campaign=abccampaign.
2. The user then clicks on a button, which redirects to a new website. The button has the following link with additional url-Parameters: websiteB.com?utm_term=button1&utm_content=newcontent

I am now looking for a skript in google Tag Manager, that uses the utm-Parameters from the advertisement (i.e. ?utm_source=facebook&utm_medium=paid&utm_campaign=abccampaign) and puts them behind the the link with the others utm-Parameters once the user clicks the button: So on the new website B, the final link should be websiteB.com?utm_term=button1&utm_content=newcontent&utm_source=facebook&utm_medium=paid&utm_campaign=abccampaign

Does anybody whether this is possible to implement without the use of cookies?