I have done some digging and, as it happens, both Alexander and Robert Munkittrick moved from Ardee to Manchester. They were brothers and the sons of another Robert Munkittrick (born 1786 died 1849) who became a pillar of Ardee society and responsible for much of the location's administration.
Firstly then - Robert. There are many records of him being a 'merchant' in Lancashire and he married Sarah Heap who was a daughter of Samuel Heap - head of a long established family in the Lancashire cotton industry - in 1842 at the Manchester Collegiate Church.
It seems unlikely that Robert could have established himself as a merchant in Manchester and found, courted and wed Sarah in less than 4 to 5 years. This places his arrival in Manchester as about 1837 and well before the 1845 Irish famine.
There are records of Alexander in Manchester which came to a head in 1849 when he sold his house as part of his eventual move to New York and into the insurance industry.
So, it looks as though first to Lancashire was Robert and he was joined by his brother, Alexander, in preparation for the latter's move to USA.
I know there is some conjecture in all this and it would be nice if someone could produce confirmatory evidence.