Question:  If a person upon wake up from sleep finds that he has a wet clothing (due to wet dream) and there is little amount of time to perform Ghusl and pray fajr Salah, due to this short of time can one perform tayammum and offer salah?

Answer: According to the narrative statement one cannot pray without performing Ghusl even if the waqt of Salah passes then you can offer qadha after the sun rise.

Please note: make sure that you have set your alarm on well before the sun rise time so that in an incident like that you will not run out of time.

Reference: [1] Fatwa Shami vol-1:234