Yes you can send a money order or check to the credit card company to pay for someone else's credit card.
You should only need the account number of the credit card and the persons name.
Put the account number on the memo section of the money order or check and then place it in the envelope along with the credit card statement.
You can also go online with the persons permission and make a payment to their credit card from your debit card through the credit card companies website and through the persons account.