Does Sharepoint maintain links between documents if they are moved?

The short answer is that if you move a file to another folder, or rename the file, any links to the file will be broken.

SharePoint itself does not keep any information about how files are related (which is why it's not a great CMS for applications that use file dependencies).

The FrameMaker SharePoint Connector adds an FMDependency field to the SharePoint list. It uses this to find and retrieve dependent files (text insets, graphics, chapters) automatically when you open an FM document.

In theory, FrameMaker could also use this information to manage file moves or renames. To do so, it would have to support those operations from within the Connector (so that it could keep the FMDependency data up to date when you change a name or path).  But it doesn't support those operations. You have to rename or move files using SharePoint directly, and then FrameMaker has no way of knowing about the changes you've made.