This script deletes any instance of the reg key "0102663e" as advised by MS Support, this key can become corrupted, leading to emails not syncing for shared mailboxes.

OutlookSharedMailboxSyncingFix.ps1

#-----------------------------------------------------------
# Fix for Shared Mailboxes Not Syncing Outlook
#
# This script deletes any instance of the reg key "0102663e"
# as advised by MS Support, this key can become corrupted, 
# leading to emails not syncing for shared mailboxes.
#
# MS bug log: 
# https://admin.microsoft.com/#/servicehealth/history/:/alerts/EX316072
# https://support.microsoft.com/en-us/office/shared-mailbox-is-not-automatically-refreshing-for-new-email-in-outlook-94b97f45-c57c-45f3-9716-f3f6bec47c73
#
# Script written by Luke Gackle                   9/3/2022
#-----------------------------------------------------------

$OutlookProfilePath = "HKCU:\SOFTWARE\Microsoft\Office\16.0\Outlook\Profiles\Outlook\"
cd $OutlookProfilePath

$searchText = "0102663e"

Get-ChildItem . –rec –ea SilentlyContinue | foreach { 
    if((get-itemproperty -Path $_.PsPath) -match $searchText)
    { 
       $key = $_.PsPath

       $keyinstance = (Get-ItemProperty -Path $key -Name $searchText)
       Write-Host $keyinstance.PSPath
       Write-Host "Deleting key..."
       Remove-ItemProperty -Path $key -Name $searchText
       Write-Host "Key deleted." -ForegroundColor Green

    } 

}

Read-Host -Prompt "Press any key to exit..."