In the present paper, a class of non-weight modules over the super-BMS3​
algebras §ϵ (ϵ=0 or 21​) are constructed. These
modules when regarded as §0-modules and further restricted as modules
over the Cartan subalgebra h are free of rank 1, while when
regarded as §21​-modules and further restricted as modules over
the Cartan subalgebra H are free of rank 2. We determine the
necessary and sufficient conditions for these modules being simple, as well as
determining the necessary and sufficient conditions for two
§ϵ-modules being isomorphic. At last, we present that these
modules constitute a complete classification of free U(h)-modules
of rank 1 over §0, and also constitute a complete classification of
free U(H)-modules of rank 2 over §21​.Comment: arXiv admin note: text overlap with arXiv:1906.07129 by other author