Generally the Administrative Appeals Tribunal Review has power to review a decision made by a delegate in relation to character including a decision not to revoke the mandatory cancellation of the visa.

The power is found in s 500 which reads :

Section 500   Review of decision

[500] (1)      Applications may be made to the Administrative Appeals Tribunal for review of:

(a)      decisions of the Minister under section 200 because of circumstances specified in section 201, other than decisions to which a certificate under section 502 applies; or

 (b)      decisions of a delegate of the Minister under section 501 (subject to subsection (4A)); or

(ba)    decisions of a delegate of the Minister under subsection 501CA(4) not to revoke a decision to cancel a visa; or

(c)      a decision, other than a decision to which a certificate under section 502 applies, to refuse under section 65 to grant a protection visa, relying on:

(i)      subsection 5H(2) or 36(1C); or

(ii)      paragraph 36(2C)(a) or (b) of this Act.

[500] (2)….

[500] (3)      A person is not entitled to make an application under subsection (1) for review of a decision referred to in paragraph (1)(b) or (c) unless the person would be entitled to seek review of the decision under Part 5 or 7 if the decision had been made on another ground.

[500] (4)      The following decisions are not reviewable under Part 5 or 7:

(a)      a decision under section 200 because of circumstances specified in section 201;

(b)      a decision under section 501;

(c)      a decision to refuse to grant a protection visa, or to cancel a protection visa, relying on:

(i)     subsection 5H(2) or 36(1C); or

(ii)    paragraph 36(2C)(a) or (b) of this Act.

[500] (4A)    The following decisions are not reviewable under this section, or under Part 5 or 7:

(a)    a decision to refuse to grant a protection visa relying on subsection 36(1B);

(b)    a decision to cancel a protection visa because of an assessment by the Australian Security Intelligence Organisation that the holder of the visa is directly or indirectly a risk to security (within the meaning of section 4 of the Australian Security Intelligence Organisation Act 1979);

(c)   a decision of a delegate of the Minister under subsection 501(3A) to cancel a visa.

Note the effect of the above is that the AAT does not have jurisdiction over decisions of the Minister personally.

Note also that the jurisdiction of the AAT is bound by the same restrictions that apply as if the matter was not a character matter. For example in relation to an offshore spouse case, the application must be made by the sponsoring spouse.

The AAT makes its decision based on the evidence in existence up to the date of its decision and can therefore take into account facts, matters and circumstances in existence at the date of hearing including new facts which occurred after the initial decision to cancel the visa (see Shi v Migration Agents Registration Authority  [2008] HCA 31; (2008) 235 CLR 286; 248 ALR 390; 48 AAR 345; 103 ALD 467; 82 ALJR 1147 & Jagroop v Minister for Immigration and Border Protection (Migration) [2015] AATA 751 (25 September 2015) at paragraph 34)

This means that good deeds done well after the initial cancellation decision can be taken into account.