[cxr]

There are two things to note, neither of which are well-advertised:

1. The parent comment you're replying to links to the main page for the Wayback Machine, which includes a Save Page Now widget, but Save Page Now actually has a dedicated page <https://web.archive.org/save/>

2. If you have an archive.org account (lets you submit and comment on collections; the library is bigger than just the Wayback Machine) and you visit the Save Page Now page while logged in, you get more options, including the option "Save outlinks"