Answer:
Yes, British territory extend all the way to the Mississippi River
Step-by-step explanation:
After the seven years war or French and War. The Treaty of Paris was signed by Great Britain, France and Spain, with Portugal in agreement, in February 1763. In the Treaty, includes many exchange of territories among the European super power, among which is the France who ceded the eastern half of French Louisiana to Britain; this includes the area from the Mississippi River to the Appalachian Mountains.
Hence, it is TRUE, that in 1763, the British territory extend all the way to the Mississippi River