Unsolicited inbound messages are messages sent in without prompting (i.e. not replies).
Replies are assigned differently than unsolicited inbound messages. Continue reading below to understand the difference.
Reply Messages
If a recipient replies to an outbound message, the reply message record will be attached back to the contact or lead the outbound message was originally sent from. The SMS will also be assigned to a user based on the "task assignment" settings in the Setup and Configuration tab.
Unsolicited Inbound Messages
If someone sends in a message without first receiving one (an unsolicited inbound message), a task will be created and assigned to the user defined in the "default record owner" setting in the Setup and Configuration tab.
Additionally, if there's an existing record with a matching phone mapping field, the task will be related to that record.