Hi Gerald.
There are many techniques to add color to a black and white photo. I'm lazy so I always try the easiest one first, i.e.
image>adjustments>match color in Photoshop. It works well most of the time.
I put every feature of the image on a separate thread: skin, eyes, mouth, hair, eyebrows, dress, jewelry. I searched Google Images for "black woman face" and selected some images that seemed to have skin tone similar to your mother's. I used a different one for the hair, for the jewelry and so on. On those photos, I very loosely selected the colors I wanted to match onto a separate layer (no need to be finicky during this step because we're only sampling the colors, not the features of the source image.). Then I used match color to match that source layer to the one in your mother's image. I set the mother-image layer's blend mode to color after the match. Finally I added color accents as required; for example I added dark brown accents to the hair and to the eye pupils. It's important to add color even to the darkest and lightest features. For example I color matched the dress to a white tee-shirt.
I give detailed instructions on color match in
this post.
I hope this helps. Don't hesitate to ask if you need clarifications.
Pierre