Is it permissible to separate the forearms from the sides during prostration after remembering to do so, or is it obligatory to complete the prostration without it? And what is the ruling if separation is not possible due to a cramped space or the presence of something supporting the elbow?

What is prescribed for a woman in prostration (sujud) is to gather herself (injima‘) and not to separate her upper arms from her sides. This separation (mujafah) is prescribed only for men, so it is not prescribed for women. This is a non-obligatory Sunnah that is not binding on a woman, whether the place is narrow or wide, or whether she remembered it from the beginning or during prostration.