We report the study of B+ -> p (Lambda) over barK(+)K(-) and B+ -> (p) over barK(+)K(+) decays using a 772 x 10(6) B (B) over bar pair data sample recorded on the gamma(4S) resonance with the Belle detector at KEKB. The following branching fractions are measured: B(B+ -> p (Lambda) over barK(+)K(-)) = (4.10(-0.43)(+0.45) +/- 0.50) x 10(-6), B(B+ -> (p) over bar Lambda K+K+) = (3.70(-0.37)(+0.39) +/- 0.44) x 10(-6), B(eta(c) -> p (Lambda) over barK(-) + c.c.) = (2.83(-0.34)(+0.36) +/- 0.35) x 10(-3) and B(B+ -> p (Lambda) over bar phi) = (7.95 +/- 2.09 +/- 0.77) x 10(-7), where c.c. denotes the corresponding charge-conjugation process.
The intermediate resonance decays are excluded in the four-body decay measurements. We also find evidence for B(eta(c) -> Lambda(1520)(Lambda) over bar + c.c.) = (3.48 +/- 1.48 +/- 0.46) x 10(-3) and B(B+-> Lambda(1520)(Lambda) over barK(+)) = (2.23 +/- 0.63 +/- 0.25) x 10(-6).
No significant signals are found for J/psi -> Lambda(1520)(Lambda) over bar + c.c. and B+ -> (Lambda) over bar (1520)Lambda K+; we set the 90% confidence level upper limits on their decay branching fractions as < 1.80 x 10(-3) and < 2.08 x 10(-6), respectively.