Ruling on Fasting While in a State of Janabah

Question
A man in a state of janabah missed the Fajr prayer due to the inability to perform ghusl because there was no hot water available, and he wanted to intend to fast the first ten days of Dhul-Hijjah. Is the intention to fast permissible? And should he make up his prayer?
Answer
I say, and with God's help: His fasting is valid even with ritual impurity, but prayer is not valid except with ablution, and God knows best.
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