Planners of churches using version 5 (or later) of WorshipPlanning.com can view messages sent to Planners and Helpers. To view messages sent to individuals, click on their name anywhere in the site, then select the "Communications To" tab. If you are an account admin (security level 3) you can see the message body of all messages. If you are security level 2 or lower, you can only see the message body of messages you sent.
By the way, the checkmark next to the date indicates that the message was successfully sent from WorshipPlanning.com. If the person claims to have not received it, there is a 99% chance it was stopped by a spam filter on their email server, or their email address is different from what's associated with their WP account.