According to Wikipedia, what happened in Pakistan was somewhat similar to what kris posted about India:
The Pakistani Rupee was put into circulation in Pakistan after the dissolution of the British Raj in 1947. Initially, Pakistan used British Indian coins and notes simply over-stamped with "Pakistan". New coins and banknotes were issued in 1948.
Also according to Wikipedia
After Indian independence, British Indian coins were in use as a frozen currency until India became a republic in 1950. The first rupee coins of the Republic of India were minted in 1950.
But at least in India, it took much longer for the old pre-independence banknotes to be demonetised, i.e. lose their official value/status:
After independence, new designs were introduced to replace the portrait of George VI. The government continued issuing the Re1 note, while the Reserve Bank issued other denominations (including the ₹5,000 and ₹10,000 notes introduced in 1949). All pre-independence banknotes were officially demonetised with effect from 28 April 1957.
So in India, it took about 7-8 years to fully/officially replace the old pre-independence currency.
I'm not sure about the demonetisation time frame in Pakistan, I couldn't find the info insofar. Wikipedia does say that the 1948-introduced Pakistani banknotes could not be redeemed in India.
The anna was demonetised in India in 1957 and in Pakistan in 1961, so the latter may be the year when Pakistan demonetised other British-era currency, but I can't be sure.