A controversial new state law is making it easier for estate executors to access digital data—such as email, photos and social-media postings—after the account holder dies.

Many Internet companies strictly limit access to their customers’ accounts to the account holder, in accordance, they say, with federal privacy law. When an account holder dies, estate executors typically have to seek a court order to access the account, which can be expensive and time consuming—sometimes taking half a year or more—and isn’t always successful.

...