Saber, welcome to the forum!
Being a Quebecer, I'm naturally interested in the many battalions which originated in Montreal but the Irish Canadian Rangers are one of the harder ones to find information about.
The Irish Canadian Rangers were assigned to the 15th Brigade of the 5th Canadian Division. This division was broken up in 1917 in England, and as has been said, the men from the Rangers eventually found their way to other Montreal units serving at the front.
Montreal, by 1916, was a difficult place to recruit new soldiers as most of those who wanted to join up had already done so. At this time Montreal had already formed the 13th, 14th, 24th, 42nd, 60th, 73rd, and 87th battalions, all of which were predominantly english speaking. The city had also supplied men for cavalry, artillery, and other ancillary units. By the time the 199th began recruiting they were in competition with the 244th, and 245th battalion for the dwindling supply of potential english recruits. So to win men over to their unit, more advertising in the form of posters had to be done. So possibly that's why so many of their posters are about today. By the way, one of their posters, #3 was sold on Ebay yesterday for $304 US link
The regiment seems to have had links with Loyola College in Montreal. This is from the Concordia University archives (Loyola merged with Sir George Williams in 1974 to form Concordia University) :"There are three plaques in the chapel vestry giving a little history of the building The chapel´s high vaulted ceilings are lined with heavy beams of BC fir. The chapel contains new colours layed up in 1976 for the Duchess of Connaught‘s Own Irish Canadian Rangers. This was a WWI regiment founded in 1914 and raised by Loyola men in 1916, which was broken up in 1917. The current colours replaced the original colours, which were brought to the Loyola Chapel in 1933. The Duchess of Connaught was the patron of the regiment, which was formed when her husband, the Duke of Connaught, was Governor General of Canada." site link
When the regiment disbanded, it's possible they gave their papers, etc to Loyola so getting in touch with Concordia University Archives could yield further information, link