No not possible. At present, each would be a different conversation with its own ID. Genesys is working on stitching the related conversations together into some form of a blob id. What you can do not is either use the customer journey API or write one ID to the other as the External Tag.
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Robert Wakefield-Carl
TTEC Digital, LLC fka Avtex Solutions, LLC
Contact Center Innovation Architect
https://www.Avtex.comhttps://RobertWC.Blogspot.com------------------------------