Is it obligatory to fulfill a vow or the intention to donate a portion of one's salary after agreeing to a transfer, in case of doubt regarding the wording of the vow or intention and the timing of recalling them?

What happened is not considered a vow (nadhr) and nothing is incumbent because of it. Doubt about the occurrence of a vow does not make it binding, as the original state is the acquittal of responsibility, and nothing becomes binding upon one's responsibility except with certainty. A vow does not become binding merely by intention; rather, its binding nature requires its verbal articulation by one who is capable of it, and it is valid with any statement that conveys commitment.