Yes but unfortunately the voice is pronouncing Muhammad rather than what is written - Mahmoud. I typed it as Muhammad a couple of times until I enlarged the font on my screen and could see the sukun. Whenever a consonant does not have a vowel, it receives a mark called a sukūn, a small circle which represents the end of a closed syllable (CvC or CvvC). It sits above the letter and no vowel should be pronounced. However, the voice on this does pronounce it which is confusing.
Technically correct, but most people would assume the duolingo response (i.e introduction: here is my son omar and my husb... etc) I would say (for your sentence): اِبْني هُوَ عُمَر وَزَوْجي هُوَ مَحْمود. By adding the ' هُوَ ', which means he is, you basically say My son, he is Omar and my husband, he is Mahmoud. This is used when like, maybe, pointing out from a list of names, etc.