  The production of a highly-polarized positron beam via nonlinear
Breit-Wheeler processes during the interaction of an ultraintense circularly
polarized laser pulse with a longitudinally spin-polarized ultrarelativistic
electron beam is investigated theoretically. A new Monte Carlo method employing
fully spin-resolved quantum probabilities is developed under the local constant
field approximation to include three-dimensional polarizations effects in
strong laser fields. The produced positrons are longitudinally polarized
through polarization transferred from the polarized electrons by the medium of
high-energy photons. The polarization transfer efficiency can approach 100\%
for the energetic positrons moving at smaller deflection angles. This method
simplifies the post-selection procedure to generate high-quality positrons in
further applications. In a feasible scenario, a highly polarized ($40\%-65\%$),
intense ($10^5$/bunch$-10^6 $/bunch), collimated ($5$mrad$-70$ mrad) positron
beam can be obtained in a femtosecond timescale. The longitudinally polarized
positron sources are desirable for applications in high-energy physics and
material science .
