Is it valid to make up for a fast for someone who intended to fast at night, then slept without eating or drinking, and woke up after Fajr, doubted his intention, then remembered it and decided to complete his fast?

If you doubt whether the intention to fast was made during the night, then the intention has not been formed, because the default is the absence of intention. If the intention to fast was made, then you intended to break it, then you intended to fast again, and you did not do anything that invalidates it, then your fast is valid according to some scholars.