Strongly simply connected algebras with super-decomposable pure-injective modules

Assume that k is an algebraically closed field of characteristic different than 2 and A is a strongly simply connected k-algebra. We show that A is of non-domestic type if and only if the width of the lattice of all pointed A-modules is undefined. Hence it follows by a result of Ziegler that A admits a super-decomposable pure injective module if and only if A is of non-domestic type, if the base field k is countable.