We examine how international transfers affect the welfare levels of a donor with a higher marginal propensity to save and a recipient with a lower marginal propensity to save when both countries adopt a pay-as-you-go (PAYG) pension system using a one-sector overlapping generations model. We demonstrate that in a dynamically efficient economy, except at the golden rule, when a per capita PAYG pension contribution of either a donor or a recipient increases marginally, the effect of the transfer on the donor’s welfare can be reduced, whereas whether the effect of the transfer on the recipient’s welfare is reduced is ambiguous. These results imply that the existence of a PAYG pension might hinder the effectiveness of the transfer on the donor’s welfare, and the adoption of a PAYG pension system is likely to cause a weak transfer paradox in which both a donor and a recipient immiserize. Our results also suggest that the introduction of a PAYG pension system, which is used as a domestic policy instrument for intergenerational income redistribution, reduces the donor’s incentive to make an international transfer to a recipient, which is a form of international income redistribution.