The Lancashire coroner will look into the deaths of eight patients at Blackpool Victoria Hospital.
The hospital has confirmed that all those who died had been inpatients on its stroke unit.
In a statement the Trust said it continues to fully support the enquiries and wants to reassure patients, in particular those on the stroke unit, that significant improvements have been made.
Mr Murphy added that he wanted "to reassure the families of any patients admitted to Blackpool Victoria and in particular the stroke unit that significant improvements have been made and the Trust continues to do everything possible to assure people that they are safe."
It's thought the events involved in the investigation date back to 2018. In December that year a number of staff were arrested over 'poisoning' claims.