How do I solve this error that occurs after assigning a record to another user
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When the security role of the old owner is just having user-level read access, this error will be thrown - since that record is owned by the new owner after the Assign operation.
The error message is bit incorrect here. The error was because the user had User Level Read Access to the record or (Entity to be specific) and on saving the record, we had one of our real-time workflow being triggered which was assigning this record to another user. And on assignment, the record being getting assigned to another user, the user who had created\saved the record was losing the access to it.