Is there a way to import Last Interesting Moment Desc and Date?

Well, not sure why you would do this because the IMs you setup would run this field.

Are you switching instances or something?

Trying to put a previous touchpoint into the IM that was captured elsewhere. Moving forward the info will be captured, but there is a currently a gap.

You may be able to import with a csv or ask Support to help.

Another option is to create a custom field "Interesting Moment Update", drop the data in there, and then trigger an IM based on that field by using the token {{lead.Interesting Moment Update}}

Yes, Josh's custom field solution will work. The date of the IM will be the date of the upload though (nothing you can do about that). 

Just another thought: if the Interesting Moment is the same for everyone there is no need to upload the actual IM text. Simply upload the Leads to a list, then select everyone on the list, then select "Lead Actions > Marketing > Interesting Moment" and type in your IM text.