The Little Company of Mary is an order of nuns founded in Nottingham, England, to care for the dying and it has now spread across the world.
You think that Sr Patrick died in 1904 "at or near Malta". It is not clear if this is Malta, Montana, or the Island of Malta. There is no reference to a convent today on the parish web page for St Mary, Malta, Montana. In the history notes about the LCM on the internet there is reference to the order having a house on the Island of Malta ca 1900.
Google provides several sites that might be of interest in a general sense, the best ones are probablywww.lcmsisters.orgwww.lcmsisters.org.uk
These two seem to take you initially to the UK, where there is a Heritage Centre. The Heritage Centre may be where the world-wide archives of the order are kept. There is a contact page on both these sites that you could use to write to the Archivist about Sr Patrick.
There is also a site that deals with the LCM in the USA -www.lcmglobal.org.usa
Again there is a contact page.
Hope this helps
Jim Lancaster (Bury, Lancs., England)