The file in question is this acptemplate: https://github.com/unkso/groupmessage/blob/master/acptemplates/__userGroupCanBeMessaged.tpl
It outputs $group->messagingAlias and $group->canBeMessaged in the checkbox. After the form is saved, the group that's being passed back to the view is not automatically refreshed, meaning it will be out of date at that moment. Instead, the view is being provided with the variables $messagingAlias and $canBeMessaged which should be output here instead, as those are always up to date versions.
Perhaps there's other sanitychecks (like $group|isset) that need to be changed to not rely on the group, but on the other variable as well.