For adding, editing, or deleting the signature in Outlook Web App, please do as follows:

1. Login your Outlook Web App on webpage.

2. Click Settings> Options at the upper-right corner. See screenshot:

3. Go ahead to click the Settings in the left bar, type your signature content into the email signature box, and then click the Save button at bottom of this webpage.

Notes:
(1) It’s optional to check the Automatically include my signature on message I send option;
(2) For editing the signature, please change the signature in the email signature box; for deleting the signature, please delete all content in the email signature box directly.
(3) For adding the signature into a composing email, please click the More > insert signature above the email. See screenshot:

Set away messages (out of office) in Outlook Web App

Change the login password of Outlook Web App (OWA)

Add contacts to distribution group in Outlook Web App (OWA)

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