If your Grocer's List DMs aren't sending on Facebook, it may be because you haven't turned on messaging for your Facebook page. To ensure messaging is turned on, follow the steps below:
Log into Facebook, then click your profile photo in the top right.
Click See all profiles, then select the Page you want to switch into.
Click your Page's profile picture in the top right of Facebook.
Click Settings & privacy, then click Settings.
In the left menu, click How people find and contact you.
Click Toggle next to Allow people to message your Page? to turn it on or off.
Note: You'll need to have full Facebook access to a Page to turn messaging on or off for your Page.