If I correctly understand your inquiry, your friend was arrested for a Probation Violation (PV) and is now awaiting his day in Court. The unidentified "They..." have offered your friend an opportunity to: (1) be released from jail until his Court date for sentencing on the PV; or, (2) stay in jail until his Court date for the PV, cooperate and write an apology letter to the Judge while in jail, then possibly be released from his probation when he appears before the Judge.
In other words, "They told him..." that he could be released prior to his Court date and then be sentenced to return to jail when he appears in Court or he could stay in jail until his Court date and then be released from his Probation when he goes to Court.
I don't know who "They..." are. I don't know the underlying conviction and sentence for which the Probation was ordered. I don't know who the is the sentencing Judge or the Court in which the PV Hearing will be conducted. I don't know the date of the PV Hearing. I don't know the prior criminal record of your friend.
I do know that your friend has elected to stay in jail, cooperate and write an apology letter to the Judge. How that letter should be written and what should be included are all determined, to a very large extent, by the unknowns I have above listed.
In general, however, your friend should honestly and openly write a letter in which: (1) he admits and acknowledges that he violated the terms of his Probation which were imposed for him to be released, in the first place; (2) he explains the reasons for his decision to violate his probation while he admits and acknowledges that his reasons are not excuses for his decision to do so; and, (3) he admits and acknowledges that he is totally responsible for the decision he made to do so (and not "...because of.." someone else's conduct or actions), that he understands the error in making that decision to violate his Probation, and that he will not make the same error if he is given another chance to be released.
Please be forewarned, however, that any promises "They..." may have made to your friend about the outcome of his PV Hearing, based upon your friend's decision to stay in jail until the PV Hearing, may not be accepted or followed by the Judge at the PV Hearing.
Good luck to you and your friend.
PLEASE NOTE: This response is not intended by the Responding Attorney to create, nor does it create, any ongoing duty for the Responding Attorney to respond to this or any other questions. This response does not form an attorney-client relationship with the Responding Attorney, nor is it intended to be anything other than a statement of the educated opinion of the Responding Attorney. This response should not be relied upon as legal advice from the Responding Attorney and is based solely upon the limited facts being provided to the Responding Attorney by the person asking the question. To the extent additional or different facts exist, this response might possibly change. Responding Attorney is licensed to practice law in the State of Ohio and, unless otherwise stated, this response is based solely upon Ohio law.