Hi Petra,
The below information has provided by SAP in Option A for EH_GENERATION_MODE.
"Each event message generates an event handler (no check in Customizing table).
In this case, you must specify the name of the function module that generates the event handlers in variable EH_GENERATION_FUNCTION".
If you want to create manually event handler in SAP EM then you can use Tcode /SAPTRX/EH_CREATE.
I just want to understand whether all basic configurations completed in SAP EM <-> SAP TM.
Can you check this discussion How to update date and status from SAP EM to TM? and check activity template FM /SAPTRX/TMS_UPDATE_FU
Regards
GGOPII