Suspended Gauteng Hawks boss Shadrack Sibiya says his role in the investigation into Richard Mdluli was motivation for his suspension.
Police Minister Nkosinathi Nhleko's lawyer said the papers "should be served" on Friday.
The foundation on Friday welcomed the Pretoria high court ruling that the police cannot unilaterally suspend Hawks boss Anwa Dramat.
The crime-fighting body announced on Thursday that it had appointed Major General Nhlamvu Elias Dlamini as acting head of the Hawks in Gauteng.
The Helen Suzman Foundation has asked the High Court in Pretoria to overturn the suspension of embattled Hawks boss Anwa Dramat.
The exact circumstances behind the suspension of the head of the priority crimes unit, Anwa Dramat, and other officials are still painfully unclear.
No one can explain why the more fearsome Hawks are investigating Dina Pule and Tina Joemat-Pettersson, but Jacob Zuma is left to police detectives.
The battle to ensure the separation of the Hawks from the police, in a case stemming from 2008, continues in the Constitutional Court on Tuesday.
The Hawks have said they will not be investigating allegations of misappropriated funds from burn victim Pippie Kruger's foundation.
Kaizer Chiefs football manager Bobby Motaung has been arrested by the Hawks for alleged fraud in connection with Mbombela Stadium's construction.
Editor and reporters have been warned that they are suspected of stealing confidential records in a case brought forward by Mac Maharaj.
Fifteen members of the Durban Organised Crime Unit - disbanded in February after allegations of a death squad - have been arrested, say the Hawks.
Crime-busting unit, the Hawks, has warned that 556 rhinos could be killed by the end of the year if current poaching trends persist.
Insiders say the case against 12 Western Cape Hawks policemen is sensitive because it could affect others in which the officers were involved.
Hawks dig in over the 'highly irregular' decision to drop charges against ex-crime intelligence boss, Richard Mdluli, writes Glynnis Underhill.
Parliamentarians have held heated final deliberations on draft legislation to restructure the Hawks in line with a Constitutional Court judgment.
The boss of the priority crimes unit is confident that the law will protect its independence.
Businessman Hugh Glenister has slammed the SAPS Amendment Bill, saying it was inadequate and will not protect the Hawks from political interference.
The NPA is set to finalise charges this week against 14 members of the Hawks who it says are linked to torture and murder.