It is okay. The mom can experiment to make sure.
In Dr Ruth Lawrence"s human Lactation textbook and LLLI they recommend up to five cups
f coffee is okay.
That amount could be a bit much, my clients seem to have done fine with a cup or two a day, no bother to the baby.
My only concern is if a mother drinks a few very large Starbucks strong coffees, drinking caffeinated soda, and eating chocolate regularly you will see a wired cranky mom and baby!