My original comment quoted below makes less sense, now that the problem has been refined

You can query the XML api to figure this out.
http://n4.nabble.com/How-can-I-tell-what-triggered-a-build-td383536.html

The upstream information is more rich than can easily be expressed in an environment variable. There's the job name and number, as well as parameters. Also, there can be multiple upstream jobs.

Can you add elements for upstream job name and build number, please?
Currently I have to parse them out from cause/shortDescription. This is fragile (format can change) and is not convenient (especially in shell scripts).

And still it is not possible to use API to set downstream build parameters, e.g. to set TAG parameter and use it in SVN checkout step.

I suggest taking your problem description to the users mailing list to see what others have done.

I see. The cause XML data doesn't have anything beside a short description

Code changed in hudson
User: : mindless
Path:
trunk/hudson/main/core/src/main/java/hudson/model/Cause.java
trunk/www/changelog.html
http://fisheye4.cenqua.com/changelog/hudson/?cs=24655
Log:
[FIXED HUDSON-5074] expose upstream cause details via remote API

Fast!