It is possible to install and use the Save to the Wayback Machine browser extension in browsers that do not have their own extension/add-on stores and are not officially supported by VerifiedJoseph.
As of February 22, 2020, the browser extension can no longer be downloaded from Opera's add-on store. To install the browser extension in Opera you must install an extension which allows you to use the Chrome Web Store.
Both Brave and Vivaldi support installing browser extensions directly from the Chrome Web Store.
The browser extension can be installed from Firefox Add-ons in Firefox forks that support WebExtensions.