Three different things that I have seen can cause green stools.

1) insufficient hind milk - this will also show as insufficient weight gain -
the stool will be very watery and sometimes foamy.  When sufficient fat is
given to the baby the stool should change right away.

2) food sensitivites to something in the mothers diet - stool is usually
normal in every way except the color - since it is always green I would
suspect something she eats a lot of like dairy or wheat.  If the offending
food is milk products it may take up to two weeks for a complete change.  If
it is wheat or some other food it could change within hours after removing
the food from the diet.

3) I have heard it said that if the mother eats a lot of green leafy vegies
the milk and stool could be green, but have never seen it myself.

Since the baby only breastfeeds for 5 minutes the obvious seems to be insuffic
ient hind milk intake.  I would want to see this baby ideally. Minimally I
would want the baby to be weighed so that we knew where that is.