The Australian Wool Testing Authority II was established under the Wool Industry Act, 1962 on 1 July, 1963. The same Act abolished the Australian Wool Testing Authority [I].

The functions of the newly established Authority were: 

(a) to carry out tests, by means of facilities provided, and
    equipment and materials supplied, by the Board, of wool and wool
    products; and 
(b) to issue certificates and make reports in respect of tests
    carried out by the Authority.
 
The authority has power to do all things necessary or convenient to be done in connection with the performance of its functions and in particular : (1) to enter into agreements to carry out tests with persons desiring the tests; (2) to advertise its services, and (3) to charge for its services such fees as it determines. The Authority has no power to acquire or hold real or personal property except moneys that become payable to it.
 
The Authority shall consist of eight members who shall be appointed by the Australian Wool Board [II] and these shall be: 

(a) a person who is a member of the Board; 
(b) a person nominated by the organisation known as the Australian
    Council of Wool Buyers; 
(c) a person nominated by the organisation known as the National
    Council of Wool Selling Brokers of Australia; 
(d) a person nominated by the organisation known as the Wool Scourer,
    Carbonisers and Fellmongers Federation of Australia; 
(e) a person nominated by the organisation known as the Wool Textile
    Manufacturers of Australia; 
(f) a person nominated by the Commonwealth Scientific and Industrial
    Research Organisation; and 
(g) two persons who, at the time of the appointment of the Authority,
    are not directly connected with the Australian wool industry. 

The membership in 1964 was : W.H. Lempriere, O.B.E. (Chairman), J.S.
Gale, R.W. Duncan, C.R. Nichols, O.B.E., S.S. Nevile, Dr. F.G. Lennox, A.E. Wallace, I. McLaren.
 
The Wool Industry Act, 1972, which abolished the Australian Wool Board [II], preserved the continuance in existence of the Authority with the only change being that the member of the Authority who was also a member of the Board was replaced by a member of the Australian Wool Corporation.
 
In 1981 the Committee of Review of Commonwealth Functions,
recommended the privatisation of the Authority. The Commonwealth Functions (Statutes Review) Act 1981 altered the status of the Authority. It became a company limited by guarantee (under the Victorian Companies Act) and ceased to exist as a Government
Authority on 6 August 1982 (Commonwealth of Australia Gazette No. S164, Friday, 6 August 1982). Its functions were subsumed on 1 July 1982 by the Australian Wool Testing Authority Limited (Primary Industry Media Release, 22 February 1982).
Historical agency address
22-28 Munster Terrace, North Melbourne
Legislation administered
Creation: Commonwealth of Australia Acts, No 99 of 1962, Wool Industry Act 1962 
Abolition: Commonwealth of Australia Acts, No 74 of 1981, Commonwealth Functions (Statutes Review) Act 1981