The cloud-based version of Outlook, Outlook Web Access, does not support the PGP Messaging Proxy. But you can use PGP Tray to manually encrypt your message:
Open Outlook Web Access and compose your email as you normally would.
Cick the PGP Tray icon.
Select Current Window, then click Encrypt, Sign, or Encrypt & Sign.
On the PGP Desktop -Key Selection Dialog screen, drag user keys to the Recipients list.
Click OK and enter the passphrase for your key. The encrypted text will appear in the email message window.
Send your message.
Assuming you have the public keys for each recipient, the appropriate keys are used automatically.