Dwyer (49) was handed a significant boost in April when the Court of Justice of the European Union ruled that the indiscriminate retention of mobile phone data for use in criminal investigations is a breach of EU law.
Phone data was a crucial part of the evidence against Dwyer as it was used to track his movements and contacts with Ms O'Hara in the lead-up to and aftermath of her disappearance in August 2012.
Remy Farrell SC, for Dwyer, told Mr Justice John Edwards at the appeal court this morning that submissions on behalf of Dwyer will be filed by July 15. He suggested the case is a priority because a number of other cases are awaiting the outcome.
Mr Justice Edwards said the Director of Public Prosecutions will require time to respond to the submissions and said it is unlikely the appeal will be heard before the court term beginning in October.
The case will be mentioned again in July to allow lawyers to update the court on what progress has been made.
Dwyer, a Cork-born architect with an address at Foxrock in Dublin, was convicted by a jury at the Central Criminal Court in 2015 of the murder of Elaine O'Hara on August 22, 2012.
His victim had been discharged from a mental health hospital hours earlier. Dwyer fantasised about stabbing a woman during sex and used Ms O'Hara to fulfil his desires.
After murdering her he disposed of some of her belongings in the Vartry reservoir in Wicklow and tried to make it look like she had committed suicide. He dumped her body in a forest where it was found in 2013.
Evidence was heard during his trial that he was sexually obsessed with stabbing a woman and had been in an abusive relationship with the vulnerable child-care worker. Much of the evidence focused on text messages between a "slave" phone used by Ms O'Hara and a "master" phone used by Dwyer and on the movements of those phones.
Dwyer appealed his conviction and argued that the use of mobile phone metadata at his trial was a breach of EU law.
The Court of Justice of the European Union (CJEU) has previously ruled that the indiscriminate retention of mobile phone traffic and location data is a breach of citizens' rights in the EU.
In his action, Dwyer claimed that data gathered from his phone, using the 2011 Communications (Retention of Data) Act, should not have been used at his trial. The Act allowed gardaí to access mobile phone data from service providers who were obliged to retain all data for two years.
The data that gardaí could access showed incoming and outgoing calls and texts and also what mast a phone pinged off at any time. The data could therefore be used to show who a mobile phone was in contact with and the approximate location of the phone at any given time.
Dwyer's lawyers argued the 2011 Act was introduced to give effect to a 2006 EU directive concerning the retention and use of data. The European Court of Justice (ECJ) found in 2014 that the directive was invalid and that position was further strengthened in subsequent rulings by that court in 2016.
The use of the data, Dwyer claimed, was unconstitutional and breached his rights under the EU Charter and the European Convention on Human Rights, including his right to privacy.
The Irish High Court ruled in Dwyer's favour but the State appealed that decision and the Supreme Court referred the case to the European Court. In April this year, the CJEU ruled that Ireland's system of retaining metadata and allowing gardaí to access it breached EU law. The decision gave the green light for Dwyer's appeal against his conviction to go ahead.
That court will hear arguments as to whether the mobile phone data should have been given in evidence at his trial and whether his conviction should be quashed.