Is the prayer of one who caught the first Tashahhud with the Imam, then stood for the second Rakʿah and did not sit for the first Tashahhud out of ignorance, then completed his prayer, valid or not?

The preponderant opinion is that what a latecomer catches with the Imam is considered the beginning of his prayer. Based on this, the questioner, after his Imam’s salutation, should have performed the second Rak’ah, then sat for the first Tashahhud, and then performed the last Rak’ah. His sitting for Tashahhud with the Imam does not suffice for the first Tashahhud because it occurred out of its proper place. Consequently, he omitted the first Tashahhud, and he should have performed two prostrations of forgetfulness (Sujud al-Sahw) for omitting the first Tashahhud. However, since the time has passed, his prayer is valid.