Change Timestamps(EXIF) name BASED on the -already- given file name!

[Nezakos]

Hey there,
I downloaded ExifTool because a member from another forum mentioned this tool. It looks that it does what I need, but I really have no idea how to do it.
Even If I'm able to use DOS commands, I can't figure out to do it here.

Well, I have thousands of photos (SCREENSHOTS) with a specific date-name. (Attached a photo).
That means I already have the ORIGINAL TAKEN DATE OF THE PHOTO.

BUT! But because the Screenshots are old, and because I did planty of Copies, Resizes, Recopies and so, the photos lost their EXIF - DATE TAKEN INFORMATION.
BUT BECAUSE I'M GEEK and NERD, I need to Re-Edit this info!

And here I need your help for this "Inverse EXIF Rename".
I use the word Inverse because most of you, asking to rename a filename based to EXIF, but I need the opposite.

I hope Exiftool tool does what I need!

Thank you in advance, Dimitrios

[StarGeek]

See FAQ #5, specifically the third paragraph that starts "Having said this".  Use the command listed under that.