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For the process builder and approval tools, you can initiate a process in Pulsar while offline. For example, you can use a custom button (Submit for Approval, for instance), and mark a checkbox field in the object indicating you would like to submit this record for approval. The process would then on the backend should be modified slightly to watch for this change to the field and kick off the process when you are online as the data syncs from Pulsar to Salesforce.
Workflow Tool - Custom Solution
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Developer Tips
When using the flow builder tool, a good rule of thumb is that if your automated process works in the Salesforce Field Service mobile app, then it will work in Pulsar.
Coordinate offline and online record updates or deletes, to avoid overwriting data. This is just the reality of dealing with a completely offline/disconnected system. The backend needs to recognize the actions were already taken by Pulsar when offline and skip repeating these actions when the data syncs from Pulsar to Salesforce.
If you want to send emails as part of your automation process, you cannot do really achieve this while offline. The emails will send be automatically sent by the process the next time you are onlinesync Pulsar.
If you use Lightning pages, Visualforce pages, or Apex triggers in your process automation, they will not work with Pulsar. Refer to VisualForce, Lightning Components, and Apex Triggers.