For Digital, go the Bot Connector route so you can use Amelia in your normal messaging flows.
About Genesys Bot Connector - Genesys Cloud Resource Center (mypurecloud.com).The Bot connector allows Genesys to maintain control of the conversation for context, transcripts, and other features.
For Voice, you probably don't have much of a choice but to transfer over to them and have them transfer back for escalation.
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Robert Wakefield-Carl
Avtex Solutions, LLC
Contact Center Innovation Architect
https://www.Avtex.comhttps://RobertWC.Blogspot.com------------------------------