It sounds like the formula being used is not working out with this little boy's digestive system. I can understand wanting to follow the dr's advice, but please know that doctors are not often very well versed in the specifics of nutrition. You would think they would be, but there are typically only one or two actual references to nutrition in the entire time they are in medical school. Our society has become so commercialized, especially with infant care, that we consider it to be "alternative" to feed the baby the way the baby was meant to be fed--at mama's breast with milk her body makes specifically for the baby it grew.
Most formulas are somewhat difficult to digest, even though they do things to the proteins to make them easier. If your friend is open to it, she could work with a lactation consultant to begin breastfeeding--once one has given birth, one has the hormonal ability to lactate. I can almost guarantee that the baby will never be constipated this way.
If she does not wish to do this, it would be wise to discuss different formulas with a nutritionist. Not knowing what formula he is on, I would not be able to say what might need changing, but I would begin with looking at whether the formula is cow's milk based or soy based. The most digestible milk other than human milk for a human baby is goat's milk, so she may wish to try a goat's milk formula.
Also, she should be sure she is using the correct formulation of water to formula, if she is using a dry powder mix.
Finally, a good probiotic that has L-Bifidus and L-Acidolphilus (Bifidus should be higher for babies than acidolphilus) can help "kickstart" his digestive system. It can be added to the formula. A little blue green algae, which contains a full spectrum of amino acids and micronutrients in near perfect balance, can also be added to the formula. These will not add calories, will help with digestion and with immune system development, and will make whatever formula is being used more complete nutritionally and more close to mother's milk.
He should not be given fruit juice, sugar, or other types of non-infant foods. What is important with formula feeding is to make the food as close as possible to what is natural and normal for human infants--which at this age would be totally provided by mother's milk. I do not mean to imply any judgement for her choice or need to use formula--however, it is important to realize that the standard of feeding is what nature gives us, and to do whatever is possible to emulate that standard.