Why Does a Specific Module, Such as Invoices, Not Appear in the “Link to Module” List?

Because this module has not been enabled in the Linked Module Configuration screen. The Link to Module list (when creating or editing a task, or linking a task to a record) displays only the modules explicitly selected from that screen. Any module that exists in the system but has not been selected there will not appear as an option, even if it is actively used in other parts of the system.