Yes, it's possible to conserve your list of favorites in Mozilla Seamonkey under Internet Explorer. Simply open the management window by clicking on "Bookmarks" then on "Manage Bookmarks." Again, the bookmark manager window will open. Click on "Tools" and then on "Export" and choose where you want to save the file. Needless to say that if you want to import a Puppy Linux Bookmark file, you choose "Import" instead of "Export."
Mozilla Seamonkey allows you to manage your Puppy Linux bookmark file to customize your favorites. For example, you can categorize sites by creating dedicated folders. You can also customize the title, add a description, include keywords you used to find the page, keep track of when you last visited the site, and even of when modifications were made. What's more is that you can turn on the viewing of this information so that it's readily available in an organized table-like format. If you click on the screen shot below, you'll see what the graphical user interface (GUI) looks like for the Puppy Linux bookmark file manager. Notice that here I'm adding information to fields for the "keyword" and "description" columns which are not populated or visible by default.