Is it permissible to fast on a Monday as an expiation for an oath (kaffarat yamin) if a person intended to fast it on Friday, then forgot the intention on Monday and remembered it after the Fajr prayer?

Obligatory fasting, including expiatory fasting, requires the intention to be made before the dawn breaks. If you do not make the intention until after dawn breaks, your fast is not valid. The intention to fast on Monday for Friday is not valid, because the intention must be made between sunset and dawn.