Answer
Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
First of all, we’d like to thank you for your question. May Allah Almighty help us all adhere to the principles of this true religion, Islam, and enable us to be among the dwellers of Paradise in the Hereafter, ameen.
Artificial insemination is generally needed in the situation when the husband is not able to deposit his semen inside his wife’s genital tract. This procedure is allowed in Islam as long as it is between legally married couples during the life of the husband.
There is no urgency to carry out artificial insemination in Ramadan while you are fasting. You can do it later.
Answering your question, we would like to cite the following fatwas published on www.islamqa.info:
Artificial insemination is not a case of necessity whereby a man and his wife may break their fast. It can be delayed until night or until after Ramadan.
What we advise you to do is to be patient and accept the decree of Allah, and to apply the Shar`i means of producing offspring. If you insist on artificial insemination then you have to take the strictest precautions to keep an eye on the sample and ensure that it is inserted immediately in your wife’s uterus by a female doctor whose religious commitment is trustworthy. And you should avoid doing this during the day in Ramadan because there is no urgency.
Allah Almighty knows best.