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It will return projects/sites that the user has checked into before. and
It will return projects/sites that have a purchase order assigned to a company (supplier, not the licensee) that the user is a staff member of. and
If the user is a staff member of the licensee, then any project for that licensee.
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When you select the site, you will see a screen similar to the one below.
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You can record an activity against a site without checking in.