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We report the results of a long-term spectroscopic monitoring of the A-type supergiant with the B[e] phenomenon 3 Pup = HD 62623. We confirm earlier findings that it is a binary system. The orbital parameters were derived using cross-correlation of the spectra in a range of 4460-4632 A, which contains over 30 absorption lines. The orbit was found circular with a period of $137.4\pm0.1$ days, radial velocity semi-amplitude $K_{1} = 5.0\pm0.8$ km s$^{-1}$, systemic radial velocity $γ= +26.4\pm2.0$ km s$^{-1}$, and the mass function $f(m) = (1.81^{+0.97}_{-0.76})\times10^{-3}$ M$_{\odot}$. The object may have evolved from a pair with initial masses of $\sim$6.0 M$_{\odot}$ and $\sim$3.6 M$_{\odot}$ with an initial orbital period of $\sim$5 days. Based on the fundamental parameters of the A-supergiant (luminosity $\log$ L/L$_{\odot} = 4.1\pm$0.1 and effective temperature T$_{\rm eff} = 8500\pm$500 K) and evolutionary tracks of mass-transferring binaries, we found current masses of the gainer M$_{2} = 8.8\pm$0.5 M$_{\odot}$ and donor M$_{1} = 0.75\pm0.25$ M$_{\odot}$. We also modeled the object's IR-excess and derived a dust mass of $\sim 5\,\times10^{-5}$ M$_{\odot}$ in the optically-thin dusty disk. The orbital parameters and properties of the H$α$ line profile suggest that the circumstellar gaseous disk is predominantly circumbinary. The relatively low mass of the gainer led us to a suggestion that 3 Pup should be excluded from the B[e] supergiant group and moved to the FS CMa group. Overall these results further support our original suggestion that FS CMa objects are binary systems, where an earlier mass-transfer caused formation of the circumstellar envelope.