This morning, Jozef Puska (31) made his third court appearance via videolink at Cloverhill District Court.
He faces "the most serious of charges", the court was told.
Mr Puska, with an address at Lynally Grove, Tullamore, Co Offaly, is charged with the murder of Ashling Murphy (23) at Cappincur, Tullamore.
The 23-year-old was fatally assaulted while out jogging along the grand canal in Tullamore on the afternoon of January 12.
Wearing a grey sweatshirt and a face mask, Mr Puska spoke to confirm his name when asked to do so by the court register.
Mr Puska also confirmed that he could see and hear the court.
A Slovakian interpreter was in court to assist him.
Judge Patricia Cronin was told by Sergeant Olwyn Murphy that formal DPP's directions were outstanding on the charge.
Defence solicitor Roy O'Neill said an investigation file was still being prepared for the DPP.
Mr O'Neill said Mr Puska was in custody for three weeks and it was "unsatisfactory" that the file was only being prepared.
He said he would "expect some progress soon".
Sgt Murphy said this was "the most serious of charges" and she expected the file would be with the DPP within 10 days.
Sgt Murphy said she expected this would be a skeleton file but it would be sufficient for formal DPP's directions to be given.
The sergeant asked for a four week adjournment.
Mr O'Neill said there was only consent to two weeks.
He said he would hope for some progress on the next date as "Mr Puska will be in custody five weeks at that stage ".
Judge Cronin further remanded Mr Puska in custody to appear before Cloverhill court via videolink on February 23.
She asked the prison officers to allow Mr O'Neill to speak to his client following the hearing, as the interpreter was available.
Mr Puska was originally brought before a special late night sitting of Tullamore district court last month charged with the school teacher's murder.
At that time, the court heard that Mr Puska was on disability benefit and defence solicitor Eoin Lysaght was assigned on free legal aid.
Ms Murphy, a talented traditional Irish musician and recent graduate from Mary Immaculate College in Limerick, was from the townland of Blueball, just outside Tullamore and was a teacher at Durrow National School.