= Solution
Label the <enamine> <carbon> bonded to <nitrogen> C1 and its <alkene> partner C2; C6 is the other <carbon> next to C1. \b[B is the C-alkylated <iminium ion> <bromide>]. Its new substituent at C2 is $\mathrm{-CH_2-C(CO_2Et){=}CH_2}$, while C1 is double-bonded to the <pyrrolidine> <nitrogen>, which bears positive charge. <bromide> is the <counterion>, accounting for Br in the <empirical formula> without requiring a retained C–Br bond.
The C2 end of the <enamine> attacks the bromomethyl <carbon> by $S_\mathrm N2$ displacement. Simultaneously, donation of the <nitrogen> <lone pair> creates the C1=N bond. This is ordinary <enamine> C-alkylation, not N-alkylation.
<proton transfer> removes an alpha <proton> at C6, converting the <iminium ion> into the <enamine> regioisomer C1=C6. That <enamine> attacks the terminal $\mathrm{CH_2}$ of the tethered acrylate in an intramolecular <Michael addition>. <nitrogen> donation restores the <iminium ion>, and <protonation> of the <ester> <enolate> completes the sequence.
The new bridge is $\mathrm{C2-CH_2-CH(CO_2Et)-CH_2-C6}$. Together with the original ring and its C1 bridge this produces the \b[bicyclo$[3.3.1]$nonane <iminium ion> skeleton] in C. It retains the <pyrrolidine> group and the <ester>; hydrolysis to a <ketone> is not part of the displayed reaction. The second panel of the original annulation figure shows the <chemical atom> connectivity and distinguishes ionic <bromide> in B from a covalent <bromine> substituent.
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