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It seems to me based on your issue that if a client is telling you they submitted on your embedded form and you didn't receive it you are probably referring to not receiving the email notification.
Have you tried logging into your account to see if the submission is there in the submission viewer?
If it's not going to your email address then you may first want to check your spam folder and additionally I would recommend these two guides below to assist you further:
If you are still having a problem with this then please provide us with a link to your embedded form so that we may investigate this problem further.