Based on what I am seeing, the LPR cannot file an N400 under the 3 yr rule if the USC spouse dies either before filing or during processing. See link from NOLO. That being said, your friend should focus more on what happens to their husband, it is tough for them going through this at this time. If the outcome end up being negative, they can deal with the I751 and look at the N400 under the 5 year rule.
Good Luck, and many thoughts and prayers for your friend and their spouse.
https://www.nolo.com/legal-encyclopedia/my-us-citizen-wife-died-can-i-still-apply-naturalize-after-three-years.html