The derangement analogue of Kurepa's conjecture

Let $p$ be a prime number. The relevant factorial sum is

$$\sum_{j=1}^{p-1}j!.$$

Derangement factorial-sum conjecture. For every prime number $p>11$,

$$p\nmid\sum_{j=1}^{p-1}j!.$$

The claim is motivated by the preceding observation relating divisibility of the infinite factorial series to its truncation and is said to resemble Kurepa's conjecture. The paper gives computations below $10^6$ consistent with the claim, but no proof.