#Yes, flaming sphere can be moved outside the original range
Yes, flaming sphere can be moved outside the original range
PHB p. 203 (Casting a Spell; Range) states:
Once a spell is cast, its effects aren’t limited by its range, unless the spell’s description says otherwise.
Regarding the specific question about flaming sphere, since the spell does not specify any limits to its range after casting, it can therefore can be moved outside of the spell's original range.