I am very sorry for the loss of your mom and father.
You should check with an attorney in your state (New Jersey).
See https://www.avvo.com
In most, if not all, states, delivery of the deed (and presumed acceptance) is essential for a valid transfer (recording of the deed is a mere formality). Regardless, a valid will devising the property would typically take precedence and be effective for a valid transfer.
In this instance, actual delivery of the deed should relate back to the date of your mom's death (when the will would have taken effect). In that case, your father's basis would be the fair market value on the date of your mother's death in 2019 (plus any improvements made after her death). Your basis would, regardless, would be the fair market value on the date of death of your father.
However, you should absolutely check with a local attorney with respect to this matter.
