What is the ruling on external artificial insemination of the womb with the husband's sperm and re-implantation into the woman's womb, and is it permissible for this to be done by a male doctor?

Artificial insemination is permissible if it is done with the spouses' [genetic] material and in the wife's womb, provided that natural conception is difficult, and that a female doctor performs the procedure, unless that is difficult, in which case a male doctor may perform it.