Is it permissible to place the wife's ovum, fertilized by the husband's sperm, in the womb of another woman, knowing that the law does not permit polygyny and the husband does not wish to divorce his first wife?

It is not permissible to implant the zygote (fertilized egg) into the womb of another woman who is not the owner of the egg, whether she is another wife of the sperm donor or a foreign woman. This is what the Islamic Fiqh Academy has decided due to the resulting confusion of lineages, loss of motherhood, and other Sharia (definition) prohibitions. Therefore, there is no benefit in the husband marrying another woman for this purpose. The questioner should be patient with her affliction, for those who are patient will receive an immense reward without reckoning.