Why You Might Want to save the messages?
In my opinion, the one major downside to using contact form 7 is that it sends all submissions to email addresses by default and does not store the messages within WordPress. I want the messages sent via contact form 7 to be stored within WordPres. So I can easily access them and I don’t have to worry about email breaking down. Another benefit here is, you don’t have to share email credentials with your staffs to make them able to access the email.(You might also accomplish this by sending email from CF7 to multiple email address simultaneously but this will use up your valuable disk space). Finally, storing contact mail on database gives easy to import feature for a wide range of format.
Fortunately, the developer has created a separate plug-in called Flamingo that can be integrated automatically with contact form 7 and collects all inbound messages.
Use Flamingo on WordPress
Go to Plugins > Add New, then search for Flamingo and install the Flamingo Plugin in your website. Once activated, Flamingo will appear on my admin main menu directly above contact. Now you can see that Flamingo provides two things, address book, and inbound messages.
Flamingo is actually a very rudimentary CRM system, that stores information on the people who contact you in an address book and then link those people to the messages they send.