If shortcuts collection collects shortcuts for the user and in Office365Import.client log file is no error message, but items are still not importing, check Office365Import.core log.
If there is bellow warning message it means that there is no message related to this one shortcut. (it should be a foreign shortcut)

2018-06-11 06:59:24Z|2047|chs-cloud-05|112| WARN|                        WriteEVShortcutsToDatabase|Shortcut Item with TransactionID [50dd3e89-2398-d75f-a2f9-b97be5df1b31] in Vault [144782B884271FA4F8CAE6B77BFAE5E251110000ev1] for mailbox container [45d33a67-37a7-40d8-910e-f01a466bad2d] could not be found in Link DatabaseHelpers. Ignoring Shortcut.
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