Simson's Brauer-Thrall 3 conjecture for finite-dimensional algebras

Let $A$ be a finite-dimensional algebra that is not of finite type, and let $\lambda$ be an infinite cardinality. An $A$-module $M$ is indecomposable if it cannot be expressed as a direct sum of two nonzero submodules.

Simson's Brauer-Thrall 3 conjecture. For any infinite cardinality $\lambda$, there is an indecomposable $A$-module $M$ of dimension

$$\dim(M)\geq \lambda.$$

This is presented as a question concerning the existence of arbitrarily large indecomposable modules over finite-dimensional algebras that are not of finite type. The supplied status is unknown.