In addition to what Gerry had already mentioned: of course, if the subsamples **B** and **C** were true random samples from the full sample, call it "population",  meaning they are "representative" then the correlation-coefficients of the smaller samples are always estimators for that of the "population", and if you use two or more random subsamples the estimated population-coefficient is somehow an average.   

But well, as you state your problem, it looks very likely to me that **B** and **C** are not such random-samples but are taken using some criterion. If such a criterion is existent then one should determine whether it distorts the randomness of the subsamples: if you take,for instance, **B** from the left edge of the whole data-cloud in a scatterplot and **C** from the right edge then the best-fit-lines in that subsamples may have completely different slopes and variances around them.