Writing the Lead Score to a Contact

We are currently in the process of building out a system integration update based on User Stories/Criteria for integrating records and data from Eloqua into our Sales system. As part of this build out, the team had intended to use the Lead Score from the Active Model to map to the Lead Score value to the contact record and then map that through the integration to Sales.

The issue is that it appears that the Lead Score model does not write to a contact field in Eloqua - at least not by default, even though there is a "Lead Rating - Combined" field. (per the help documentation: Contacts: Lead Scoring fields in Eloqua (