Avatars are incorporated into the user module of that import system. There isn't a separate avatar module. If the avatars failed to import then perhaps you entered the wrong paths on the config step. It asks you for the paths to data and internal_data for the source forum. That is where avatars are stored.
In general, you'd want a full absolute path (/home/site/public_html/forums/data, for example). Otherwise, you can write a relative path, but it needs to be relative based on the directory XF has been installed in (the one you are running the import on).
Note that if you're importing from a totally different site on the same server, you may need to download the files from their old location and reupload them to the "target" site (and enter the new path).