Question Summary:
Is it allowed for women to give Dawah?

Question Detail:

Is there any specific ways a woman can give Dawah, how important is it for a woman to give Dawah in Islam, is there any restrictions/conditions?
does a woman obey her husband or can she do as she pleases and give Dawah without disturbances?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
 
Daw`ah has been the foremost responsibility of every prophet. Among the three missions of Rasulullah ﷺ, Da`wah has been enumerated through the recitation of the Qur`an-e-Kareem.[1]
Every Muslim, male and female is tasked with the responsibility of Da`wah.[2] However, while acknowledging the great merits of Da`wah, we should also guard ourselves from all forms of fitnah especially when using modern technology such as the internet etc. for Da`wah. The strong possibility of fitnah through facebook, chat rooms, etc. cannot be ignored. Many sincere people have used these forms for Da`wah but got caught up in some form of illicit and immoral relationship with the opposite gender.<sup>[3]</sup>   
The principle of Shari`ah is that preference must be given to basic responsibilities. A married woman`s basic responsibility is towards her husband and family. In giving Da`wah, it is not permissible for a married person to infringe on the marital rights.^[4]
It is therefore best for a woman to consult with her husband^[5] before engaging in any Da`wah activity to ensure he is also comfortable and his rights are not compromised.[6]
 
And Allah Ta’āla Knows Best
AbdulMannan Nizami
Student Darul Iftaa
Chicago, USA 
Checked and Approved by,
Mufti Ebrahim Desai.
www.daruliftaa.net