You need to specify the package name before the class name (then you may write it without the package) like this:
./adb shell am broadcast -a android.intent.action.BOOT_COMPLETED -c android.intent.category.HOME -n net.fstab.checkit_android/.StartupReceiver
Practically it turns out that you just have to add a slash after the package name.
You helped me start, I helped you finish 🙂