Yes, through your browser. Zoho Books is online accounting software, so it runs the same in Firefox or Chrome on Linux. The only desktop app Zoho offers is a Windows one you do not need.
Zoho Books by Zoho · Business & accounting · Works in a browser
Zoho describes Books as online accounting software, and the browser version is the real product. Signing in
on a Linux machine gets you the same invoices, bank feeds, reports and tax settings you had on Windows,
because none of it was ever stored on your computer.
Zoho does publish a Windows desktop app through the Microsoft Store, along with iPhone and Android apps.
There is no Linux desktop app. That is not a loss worth worrying over, since the desktop version is a
window wrapped around the same site.
Accounting data is the kind of thing worth being careful with, so before you leave Windows, sign in from the
Linux machine once while both computers still work and confirm you can reach everything. Also check where
your two-factor sign-in codes arrive, because being locked out of your books at tax time is the one
expensive mistake here.
If you would rather not be on a subscription at all, GnuCash is free, installed on your own machine and does
proper double-entry bookkeeping. It expects more accounting knowledge from you than Zoho Books does.
Free double-entry accounting that lives on your own computer, with invoices, bills and reports. Plainer looking and it assumes you know some accounting.
Your files: Cannot open Zoho Books data directly. Imports the CSV files you export from Zoho, with categories usually needing tidying.