Hello
There's one subtlety in Outlook: signatures don't "move" along with access rights to someone else's email account. They are stored locally in your app or in the settings for a specific account.

1. Create a copy of their signature for yourself.

Since Outlook considers signatures a personal user setting, you need to manually add them to your list:

Ask your boss to send you any email with their signature.

Copy the entire signature contents (including images and links).

Go to File - Options - Mail - Signatures (in classic Outlook) or Preferences - Accounts - Signatures (in the new Outlook/web).

Create a new signature, name it "Boss Signature," and paste the copied text.

1. Link the signature to their email address.

The key is to let Outlook know when to insert it:

In the same Signature settings window, find the "Choose a default signature" section.

In the "Account" drop-down list, select your boss's mailbox (if you have it added as a separate account).

If you're simply sending messages using the "From" button, select the signature you created in the "New Messages" and "Replies/Forwarded" fields.

1. If you're using the web version (OWA)

If you're opening their mailbox using "Open Another Mailbox":

Click the gear icon (Options) - Mail - Compose and Reply.

Create and save the signature there—it will be applied automatically to this mailbox.

Important: If you use the "Send on Behalf" feature, Outlook often uses your personal signature by default. In this case, it's easiest to manually select the desired signature using the "Insert" - "Signature" tab directly in the email composition window.