Just so I understand the terminology you are using:

• you have Thunderbird on your computer
• you have two email addresses defined: e.g. tls@xyz.net and boss@xyz.net; each has an Inbox, etc.

Your boss has her own computer:

• she has Thunderbird on her computer
• she has two email addresses defined: e.g. tls@xyz.net and boss@xyz.net; each has an Inbox, etc.

If this is a correct understanding, then on her computer:

• you need to set her signature (if you haven't already done so)
• right click on your email address (tls@xyz.net) then 'Settings'
• at the lower left of the Settings screen, pull down 'Account Actions' and click 'Remove Account'

On your computer:

• right click on her email address (boss@xyz.net) then 'Settings'
• at the lower left of the Settings screen, pull down 'Account Actions' and click 'Remove Account'

Now your computer will have only your email, and hers will have only hers.

Is that what you wanted?

That is exactly what I was asking and thank you very much. tlscott65 said

I downloaded Thunderbird to be able to customize my email signature, which I have done. I created the signature for my boss and now I can get to both accounts. I want to be able to only get into my account and my boss able to only get into her account. Please help.