In Salesforce Lightning Experience, when a user changes the Assigned To field on a Task to transfer ownership to another user, the assigned user may receive two duplicate email notifications instead of one. This behavior can occur whether the field is updated manually by a user or automatically through Process Builder.
This is a known behavior in Salesforce Lightning Experience (LEX). Salesforce Engineering is tracking a fix for this issue under investigation W-5158938 (subject: Fix email notifications for assigned tasks in LEX).
As a workaround, consider the following options:
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