You cannot make a charitable donation to another person, only to a qualified charitable organization. If it is your employer, it would not be a gift.
Your employer should include the amount that is over $5,250 in your box 1 wages on your W2 as taxable income. If this is included in your income, then yes, you can take an education credit for the amount you are considered to have paid. The first $5,250 would not be able to count towards the education credit as you are not taxed on that income so you would be getting a double benefit.
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