Praise be to Allah.
It is permissible for a woman to pray when mucus is coming out of her mouth, rather it is obligatory for her to offer the prayers on time, and that is not an impediment to her praying.
You should understand that mucus and spittle do not invalidate wudu, and they are pure. The Prophet (peace and blessings of Allah be upon him) allowed a worshipper to spit into his garment or under his foot whilst praying. (Al-Bukhari, 500)
For more details, please refer to the following answers: 2176 , 174361 , 1999 , 44633 .
And Allah knows best.
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