The Attorney-General is seventh in the line of succession to the Presidency of the United States.
Does an Acting Attorney-General replace the former Attorney-General in the line of succession?
The presidential line of succession is governed by the U.S. Constitution, specifically Article II section 1:
In Case of the Removal of the President from Office, or of his Death, Resignation, or Inability to discharge the Powers and Duties of the said Office, the Same shall devolve on the Vice President, and the Congress may by Law provide for the Case of Removal, Death, Resignation or Inability, both of the President and Vice President, declaring what Officer shall then act as President, and such Officer shall act accordingly, until the Disability be removed, or a President shall be elected.
The 25th amendment reinforces this and says "Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress."
So, after the vice president, the constitution lets Congress pass laws governing the rest of the succession. This is governed by the Presidential Succession Act.
3 U.S. Code Chapter 1, Section 19 lays out the rest of the line of succession: Next come the Speaker of the House of Representatives (subsection a) and the President pro tempore of the Senate (subsection b) and "then the officer of the United States who is highest on the following list, and who is not under disability to discharge the powers and duties of the office of President shall act as President: Secretary of State, Secretary of the Treasury, Secretary of Defense, Attorney General, Secretary of the Interior, Secretary of Agriculture, Secretary of Commerce, Secretary of Labor, Secretary of Health and Human Services, Secretary of Housing and Urban Development, Secretary of Transportation, Secretary of Energy, Secretary of Education, Secretary of Veterans Affairs, Secretary of Homeland Security" (subsection d).
So you have the Attorney General at number 7. However, the next subsection says the following (emphasis mine).
(e) Subsections (a), (b), and (d) of this section shall apply only to such officers as are eligible to the office of President under the Constitution. Subsection (d) of this section shall apply only to officers appointed, by and with the advice and consent of the Senate, prior to the time of the death, resignation, removal from office, inability, or failure to qualify, of the President pro tempore, and only to officers not under impeachment by the House of Representatives at the time the powers and duties of the office of President devolve upon them.
I think the bolded text answers your question. The Acting Attorney General has not been confirmed by the Senate, so is not in the presidential line of succession.
Now there is potentially room to argue that, if the Acting Attorney General has been confirmed by the Senate for some other office (most likely Deputy Attorney General), then they qualify. Of course, there is no case law to clarify this, since the presidential succession has never gone beyond what is listed in the constitution. However, I don't think it's a very compelling argument, particularly for the current Acting Attorney General who was not appointed on the basis of his previous confirmation.
(Interestingly, a Bill was introduced to the House in 2003 that would have explicitly removed acting officers from the line of succession. Ultimately, that Bill did not progress.)
A cabinet member is only a cabinet member when they are confirmed not just because they are temporarily doing a cabinet member’s job.