  In this paper, we obtain the explicit expression of the supersymmetric
algebra associated with the recently proposed massive supermembrane including
all surface terms. We formulate the theory as the limit of a supermembrane on a
genus-two compact Riemann surface when one of the handles becomes a string
attached to a torus. The formulation reduces to a supermembrane on a punctured
torus with a "string spike" (in the sense of \cite{dwln}), attached to it. In
this limit, we identify all surface terms of the algebra and give the explicit
expression of the Hamiltonian in agreement with the previous formulation of it.
The symmetry under area preserving diffeomorphisms, connected and nonconnected
to the identity, is also discussed. Only parabolic $Sl(2,\mathbb{Z})$ discrete
symmetries are preserved.
