Answer:
Yes, the court can hear this petition.
Step-by-step explanation:
According to the Suspension Clause of Article I, Section 9, Clause 2, Detainee like the case above actually has the right to file/propose a file a habeas corpus petition even if that person held the status as a 'criminal' (unless the privilege is directly suspended because that person possess high level of threat).
When united states has sovereign control over a territory, the united states gained an influence over the judiciary branch of that territory. Because of this, the suspension clause is also applicable in that territory.