1940 S Lincoln Wheat Ear Penny With Die Crack Reverse

Looks like a nice example.

64/65RD

You say this all of the time, and I don't get it at all. It's clearly a Die Crack. Anyways, for the grade, I would say MS-63.

Although interior die cracks do occur they are rather unusual, particularly for 20th century coins.
I base my opinion on the fact that the feature doesn't extend into the fields, never mind to the rim.

I visualize a metal thread from something like a wire brush getting into the striking chamber when a previous coin was struck.
That item when struck imparted its image on both a previous coin and the die.
After that the item fell out and all subsequent coins were struck with the now altered die.

Occam's razor (also Ockham's razor or Ocham's razor; Latin: lex parsimoniae "law of parsimony") is the problem-solving principle that the simplest solution tends to be the right one. When presented with competing hypotheses to solve a problem, one should select the solution with the fewest assumptions...= die-crack.

KK

It goes to the rim so it's a die crack. No reason to think it's die damage IMO.

MS-64RD.

Plus a faint Greasy Ghost on the rev.

Progressive Indirect Design Transfer: A form of Die Deterioration that manifests itself in the form of a "ghostly" image of a design element on the opposite side of a coin. The force of a die strike travels through the planchet and into the opposite die. After hundreds of thousands of strikes, the outline of the designs begin to transfer to the opposing die and show on the coins that are struck. In the case of Lincoln cents, it is common to see a ghostly outline of Lincoln's bust on the reverse of wheat cents that are struck in later die states. It is especially visible on uncirculated coinage. This should not be confused with a die clash or a "greasy ghost."