Background: Several studies have indicated that anti-SARS-CoV-2 mRNA vaccinations are less effective in inducing robust immune responses among solid organ transplant recipients (SOTRs) compared with the immunocompetent. The third dose of vaccine in SOTRs showed promising results of immunogenicity, even though clinical studies have suggested that immunocompromised subjects are less likely to build a protective immune response against SARS-CoV-2 resulting in lower vaccine efficacy for the prevention of severe COVID-19. Methods: Serological IgG and IgA were analyzed through CLIA or ELISA, respectively, while Spike-specific T cells were detected by ELISpot assay after the second and third dose of vaccine in 43 SOTRs. Results: The third dose induced an improvement in antibody response against SARS-CoV-2. We also reported a strong correlation between specific humoral and cellular responses after the third dose, even though we did not see significant changes in the magnitude of the SARS-CoV-2-specific T cell response. SOTRs who contracted the SARS-CoV-2 infection after the third dose, despite eliciting a positive IgG response, failed to mount an anti-Spike-S1 IgA response, both after the third dose and after SARS-CoV-2 infection. Conclusions: We can conclude that serum IgA detection can be helpful, along with IgG detection, for the evaluation of vaccine efficacy, principally in fragile subjects at high risk of infection.