Nothing conflicting.
14 CFR 61.153
Sec. 61.153
Eligibility requirements: General.
To be eligible for an airline transport pilot certificate, a person must:
(a) Meet the following age requirements:
(1) For an airline transport pilot certificate obtained under the aeronautical experience requirements of §§ 61.159, 61.161, or 61.163, be at least 23 years of age; or
(2) For an airline transport pilot certificate obtained under the aeronautical experience requirements of § 61.160, be at least 21 years of age.
(b) Be able to read, speak, write, and understand the English language. If the applicant is unable to meet one of these requirements due to medical reasons, then the Administrator may place such operating limitations on that applicant's pilot certificate as are necessary for the safe operation of the aircraft;
(c) Be of good moral character;
(d) Meet at least one of the following requirements:
(1) Holds a commercial pilot certificate with an instrument rating issued under this part;
(2) Meet the military experience requirements under Sec. 61.73 of this part to qualify for a commercial pilot certificate, and an instrument rating if the person is a rated military pilot or former rated military pilot of an Armed Force of the United States; or
(3) Holds either a foreign airline transport pilot license with instrument privileges, or a foreign commercial pilot license with an instrument rating, that--
(i) Was issued by a contracting State to the Convention on International Civil Aviation; and
(ii) Contains no geographical limitations.
(e) After July 31, 2014, for an airline transport pilot certificate with an airplane category multiengine class rating or an airline transport pilot certificate obtained concurrently with an airplane type rating, receive a graduation certificate from an authorized training provider certifying completion of the airline transport pilot certification training program specified in § 61.156 before applying for the knowledge test required by paragraph (g) of this section;
(f) Meet the aeronautical experience requirements of this subpart that apply to the aircraft category and class rating sought before applying for the practical test;
(g) Pass a knowledge test on the aeronautical knowledge areas of Sec. 61.155(c) of this part that apply to the aircraft category and class rating sought;
(h) Pass the practical test on the areas of operation listed in Sec. 61.157(e) of this part that apply to the aircraft category and class rating sought; and
(i) Comply with the sections of this subpart that apply to the aircraft category and class rating sought.
There is no straight conversion for any license other than private. You have to take the written and practical test. Even for commercial you would have to do a written and practical test.
Of course most of us fail on para C.