Yes. You can operate the same email account from many different devices. Many of us use a smartphone or tablet to manage email alongside a more traditional laptop or desktop computer. I have several email accounts, all of which are set up and operated via a Windows laptop, a Linux laptop, a Linux desktop, an Android tablet and a Blackberry smartphone.

For both your PC and Laptop to show you the same data, you need both to be using IMAP. The availability of this depends on your email provider. The email services offered by some ISPs still use only POP, which would not work so well for you.

One consideration is that even if your mail provider offers IMAP, they may not support both computers being connected to the email at the same time.

If you tell us who provides your email, someone could advise if IMAP is available to you.

Frontier is the server, I use Thunderbird Mozilla

i do know it ssays (for Frontier email) pop.3 server

Looking at this site:

https://frontier.com/helpcenter/internet/using-your-email/other-email

I see references to POP. They specifically mention the need to set your email program to leave messages on the server if you want to read email via two or more devices. So this is not ideal for multi-device use.

They also mention that some of their email services are provided by yahoo. Now, yahoo DO provide IMAP, though they don't necessarily advertise it or encourage its use. My own experience with service subcontracted out to yahoo is that even if your ISP don't offer a particular service, you can set up the yahoo servers in your email program instead of those published by your ISP and thereby make use of the full range of services. In my case I used to work a bt.com account (underwritten by yahoo) by going directly to yahoo. So if you are one whose frontier mail is actually handled by yahoo, you may be in luck (as far as availability of IMAP is concerned, at least; I don't have too much respect for the quality of yahoo's email provision)

You don't have to be limited by what your ISP offers. Googlemail, GMX and others offer free IMAP-connected email systems. You can probably get your frontier account to forward to an alternative provider, and you can probably register your frontier account with another provider, so you can continue using the frontier address even if it's actually connected to and relayed by another provider. Both GMX and gmail offer these capabilities.

I'm mostly interested in having Thunderbird Mozilla on both computers...and have it the same. DOES Thunderbird allow this? Can I open my account on either (not concurrently)?

I think I stated my question incorrectly. I just downloaded Thunderbird and tried what i am trying to achieve. Didn't work. I want to have them merge. So when I open my Thunderbird account on laptop, it has all my folders and messages just the same as when I open it on the PC in the office. One account, able to be seen and handled on 2 different devices (Not at same time, of course) Does this make sense?

If you read the previous answers you will see that you need an IMAP email account to do what you want. If your provider only offers POP then no email client can change that. Thunderbird is email client software. You can install it on as many devices as you like. It cannot change the operating mode of your providers email service.

I had deleted emails from secondary PC before primary PC failed. Secondary PC no longer has the primary PC's emails. How can I get the emails on the primary PC to the secondary PC? thanks in advance for your help