Currently there is no direct way to do it. However you could run a script which runs the following to extract the Run ID from the spool file and set a global variable.
sendevent -E SET_GLOBAL -G RUNID=`autosyslog -t S -J adf1_pipeline_parameters_FAIL | grep "Run ID: " | awk '{printf $4}'`
The above example will extract the Run ID from the spool file for the adf1_pipeline_parameters_FAIL job and use sendevent to set a global variable RUNID in AutoSys. In the successor job you would use the global variable RUNID as the parameter value. The example will work with UNIX and Linux machines.
Since this use case is not handled directly in the product, can you open a enhancement request with support.