The {\it{Polaron measure}} is defined as the transformed path measure $$\widehat{\mathbb P}_{ε,T}= Z_{ε,T}^{-1}\,\, \exp\bigg\{\frac{1}{2}\int_{-T}^T\int_{-T}^T\frac{ε\e^{-ε|t-s|}}{|ω(t)-ω(s)|} \,\d s \,\d t\bigg\}\d\mathbb P$$ with respect to the law $\mathbb P$ of three dimensional Brownian increments on a finite interval $[-T,T]$, and $ Z_{ε,T}$ is the partition function with $ε>0$ being a constant. The logarithmic asymptotic behavior of the partition function $Z_{ε,T}$ was analyzed in \cite{DV83} showing that $$ g_0=\lim_{ε\to 0}\bigg[\lim_{T\to\infty}\frac{\log Z_{\eps,T}}{2T}\bigg]=\sup_{\heap{ψ\in H^1(\R^3)}{\|ψ\|_2=1}} \bigg\{\int_{\mathbb R^3}\int_{\mathbb R^3}\d x\d y\,\frac {ψ^2(x) ψ^2(y)}{|x-y|} -\frac 12\big\|\nabla ψ\big\|_2^2\bigg\}. $$ In \cite{MV18} we analyzed the actual path measures and showed that the limit ${\widehat {\mathbb P}}_{\eps}=\lim_{T\to\infty}\widehat{\mathbb P}_{\eps,T}$ exists and identified this limit explicitly, and as a corollary, we also deduced the central limit theorem for $(2T)^{-1/2}(ω(T)-ω(-T))$ under $\widehat{\mathbb P}_{\eps,T}$ and obtained an expression for the limiting variance $σ^2(\eps)$. In the present article, we investigate the {\it{strong coupling limit}} $\lim_{\eps\to 0} \lim_{T\to\infty} \widehat{\mathbb P}_{\eps,T}=\lim_{\eps\to 0} \widehat {\mathbb P}_\eps$ and show that this limit coincides with the increments of the stationary Pekar process with generator $$ \frac 12 Δ+ \bigg(\frac{\nablaψ}ψ\bigg)\cdot \nabla $$ for any maximizer $ψ$ of the free enrgy $g_0$. The Pekar process was also earlier identified in \cite{MV14}, \cite{KM15} and \cite{BKM15} as the limiting object of the {\it{mean-field Polaron}} measures.}