We investigate underwater optical communication system that is relayed by a single decode-and-forward (DF) relay through an exponential-generalized Gamma distribution (EGG) into a final destination. Specifically, a certain terminal device sends data through underwater wireless optical link (UWO) that utilizes the so-called blue laser technology into a nearby relay that in term sends a decoded (and modulated) version of the received signal into a remote destination. The RF link is assumed to follow the generalized $α-μ$ distribution; which include many distributions as a special cases, e.g., Rayleigh. In the other hand, the UWO link is presumed to follow the state-of-art Exponential-Generalized Gamma distribution (EGG) which was recently proposed to model the underwater optical turbulence. Closed-form expressions of outage probability, average error rate and ergodic capacity are derived assuming heterodyne detection technique (HD). Also, asymptotic outage expression is obtained for more performance insights. Results show that high achievable rate is obtained for high-speed underwater communication systems when turbulence conditions underwater are relatively weak. In addition, the RF link is dominating the outage performance in weak optical turbulence while UWO link is dominating the outage performance in severe optical turbulence.