  We prove that the Fourier transform of the properly-scaled normalized
two-point function for sufficiently spread-out long-range oriented percolation
with index \alpha>0 converges to e^{-C|k|^{\alpha\wedge2}} for some
C\in(0,\infty) above the upper-critical dimension 2(\alpha\wedge2). This
answers the open question remained in the previous paper [arXiv:math/0703455].
Moreover, we show that the constant C exhibits crossover at \alpha=2, which is
a result of interactions among occupied paths. The proof is based on a new
method of estimating fractional moments for the spatial variable of the
lace-expansion coefficients.
