FAXing over VoIP networks doesn't work. You can sometimes arrange things so a fairly high percentage of FAXes get through OK. You can occassionally create setups that work 100% of the time. These are rare and unrepeatable setups. You need to use a proper FAX over IP protocol, such as T.38, to achieve consistent reliable FAXing across IP networks.
If using the Outlook Windows client and cannot send email as a shared mailbox. Switch off Cached Exchange mode. This will force Outlook to use the GAL permissions for send as instead of (likely) out of date cached local permissions.