Using Classic Outlook on Windows for personal email, calendar, and contact management
WOW! Today is the day, for me!!! I've discovered that I finally have this option inside the New Outlook client!!!
*** NOTE: SEE Ehret Michael's note below - this was his discovery, herein:
Now, there is a checkbox in the settings which allows disabling the deleting of invite messages.
Navigate to View > View settings > Calendar > Events and invitations and unselect "Delete invitations from inbox after responding" in section "Invitations from other people".