Yes. The checks were to vlnaes2.
The money is presumed a loan because the professor gave money to vlnaes2, vlnaes2 accepted the money, and vlnaes2 is not related to the professor. The law presumes loan (read the case linked to on page 2).
Absent any written contract or expressed terms of repayment, the court can provide loan repayment terms, as justalayman noted earlier (pay on demand or pay within a reasonable amount of time).
It is because, absent express payment terms, the loan potentially could be paid back all at once that the statute of frauds is not a factor.
Once again, it would be nice to know how much money was given to vlnaes2 by the professor.
At any rate, it appears vlnaes2 will be left with the task of proving with clear and convincing evidence that the money was a gift or payment for services performed.
I suggest vlnaes2 respond to the attorney letter (or better, have vlnaes2's own attorney respond to the attorney letter) by saying the letter was received and no money is owed - or say nothing at all (possibly best) and wait to be sued.
Vlnaes2 can work with his/her own attorney on a defense should vlnaes2 receive a summons and complaint.