Dispatching would require you to know who the form will be sent to next. Dispatching would allow you to setup a question in the form, where if you needed to send it to a specific user, that userID is entered into this field and the form is sent to them. After the submission is complete, the users is sent the form and there are other destinations that will process, usually an email notification.
In Teamwork, it would work differently, where you could allow the users to Transfer the form to the Teamwork "bucket" or to an individual directly. You can save to the bucket by selecting the Close button (on iOS) and selecting Transfer. This would allow users, with access, to search for the forms and claim them. If this option is not configured, please see the following doc to get details on setting up Teamwork: https://docs.prontoforms.com/1374411/Content/Features/PF_Teamwork/TeamworkH3/Configuration/StepsEnablePFTeamwork.htm?Highlight=teamworkYou can configure an additonal email destination on this form to trigger when the form is in an "Incomplete" state. This incomplete state processes when the form is transferred into the "bucket" and is not submitted.These settings are found when editing the email destination and selecting the Filtering tab. In that tab, there is a section to set the Filter rules for the Form Submission State.In your scenario, I would see the Teamwork option as being the best solution. It allows the flexibility of sending it to a person directly or transferring to the searchable bucket. All of this would also include notifications setup with an email destination. These destinations can either have a preset mailbox destination - a general email list that allows for visibilty or use a question within the form to send the notification.I hope this helps.