So the Letter to the Hebrews is not accepted as authentic?
The Letter has had an interesting history.
Initially, it seems it was always anonymous, and because of that, it was not immediately accepted as canonical. Eusebius (c325) classed it as antilegomena
(Gk. spoken against, or disputed). It gained acceptance primarily because of its theology.
Really it was only much later that it started to be attributed to Paul, perhaps in an attempt to provide apostolic pedigree.
As Origen observed, Hebrews "does not exhibit the characteristic roughness of speech or phraseology admitted by the Apostle [Paul] himself, the construction of the sentences is closer to the Greek usage, as anyone capable of recognising differences of style would agree. On the other hand the matter of the epistle is wonderful, and quite equal to the Apostle's acknowledged writings: the truth of this would be admitted by anyone who has read the Apostle carefully... If I were asked my personal opinion, I would say that the matter is the Apostle's but the phraseology and construction are those of someone who remembered the Apostle's teaching and wrote his own interpretation of what his master had said. So if any church regards this epistle as Paul's, it should be commended for so doing, for the primitive Church had every justification for handing it down as his. Who wrote the epistle is known to God alone: the accounts that have reached us suggest that it was either Clement, who became Bishop of Rome, or Luke, who wrote the gospel and the Acts." (This is Origen quoted by Eusebius in The History of the Church
As for the author?
Among various contenders – Clement of Rome, Barnabas, Paul, Luke, Apollos, or his teacher Priscilla.
For no good reason I can argue, I favour the idea it was written by Priscilla, scholars date it around 64-65. Priscilla, along with her husband Aquila, were active from very early, contemporary with Paul, and instructors of Apollos. It may well be that her authorship was suppressed because she was a woman.