Assalamualaikum ustaz. A husband who is the imam of his wife forgets the recitation of the surah he’s reciting in prayer. Is it permissible for his wife to correct his recitation? Hope for an answer.
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions and all those who follow his footsteps until the Last Day.
Basically, correcting the mistake made by the imam is sanctioned in congregational prayer as stated by the Messenger PBUH:
التَّسْبِيحُ لِلرِّجَالِ وَالتَّصْفِيقُ لِلنِّسَاءِ
“Saying ‘Glory be to God’ applies to men and clapping to women.” 
According to the above hadith, the scholars’ opinions are:
- Imam al-Nawawi stated according to madhhab al-Syafie, tasbih (glory be to God) for men and clapping hands for women. 
- In Imam Mawardi’s opinion, clapping hands is a way for a woman to correct the imam because the voice of a woman is aurah, there is concern that it will be a fitnah on those who hear it. And he said that clapping hands is more accurate compared to tasbih for women according to the above hadith. 
- While in madhhab Imam Malik, it is stated that for both men and women it is tasbih and restricted clapping hands for women in prayer. 
Hence, according to the above discussion, for madhhab Syafie, correcting the imam is by tasbih for men while women do so by their hands.
Furthermore, scholars agreed that a makmum should rectify and correct the imam if he made a mistake or forgot the recitation of al-Quran or other actions in prayer. 
Ibn Hajar al-‘Asqalani stated the restriction of tasbih (loudly reciting Subhanallah) by women is due to the fact they are commanded to lower their voices in prayer to avoid fitnah, while men are restricted from clapping for it is synonymous with women. 
While according to Ibn Abd al-Barr, he cited the opinion of some scholars which stated the reason tasbih is makruh (discouraged) for women and the permissibility of clapping to correct an imam is that the mellow voice of most women and may distract the concentration of the male congregants. 
According to Imam al-Zarkasyi, clapping to correct the imam is when it is in a situation where there is ajnabi man; whilst when it is a congregational prayer of just women or men who are her mahram, then they should recite tasbih through jahar (loud and clear). 
This is also the fatwa issued by Syeikh Nuh ‘Ali Salman and Syeikh Abdul Aziz bin Baz, where it is permissible for a woman to correct the imam if the one present is her husband, other women or other men who are her mahram. Moreover, Syeikh Ibn Baz also permitted a woman to correct an imam in congregational prayer if no other men did so. The voice of a woman is not aurah and it only becomes aurah if she purposely softens or mellows her voice and this is prohibited. 
We chose the opinion which permits a woman to correct the imam by reciting tasbih if the imam made a mistake or correcting the recitation of the imam if he forgets on the condition that she is praying with her husband, other mahram men or with other women. However, it is prioritized to correct him by clapping her hands.
As for congregational prayer with other ajnabi men, then she is prohibited from correcting with tasbih, rather she should correct him by just clapping her hands.
 See the link https://bit.ly/2FS3pyr and http://aliftaa.jo/Question3.aspx?QuestionId=2202#.XE5-sVwzZPZ