One of the basic rules of probation is to obey all laws. Fortunately, minor traffic violations cannot be used as the basis of a probation violation. This includes your friend's seat belt ticket. See Penal Code 19.8.
If your friend has to check in with a probation officer, she is on formal probation. (Informal probation is essentially the judge saying, "Don't let me see you in my courtroom with new charges again," and does not involve a probation officer.)
Your friend's probation conditions may also require her to report any police contact to the probation officer. She should carefully review her terms and conditions, and report the ticket if she is required to do so. Since she can't be violated for a seat belt ticket, it makes no sense to fail to report it.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
Mr. Marshall is correct in that minor traffic violations cannot be used as the basis of a probation violation. However, since it is so minor it would not hurt to report it to her probation officer.