As per https://wiki.jenkins-ci.org/display/JENKINS/Parameterized+Build :

To use a Run Parameter, the value should be in the format jobname#buildNumber (eg. "&MyRunParam=foo-job%2399" for foo-job #99)

But when I pass the same from MultiJob Phase, it is not working. The Downstream Job always throws this error..

ERROR: Unable to find a build for artifact copy from: RUN_JOB

When I do the same with "Trigger/call builds on other projects", it works. The downstream job is able th understand the value for Run Parameter.