  In continuation of [1] we study associated primes of Matlis duals of local
cohomology modules (MDLCM). We combine ideas from Helmut Z\"oschinger on
coassociated primes of arbitrary modules with results from [1], [4], [5], [6]
and obtain partial answers to questions which were left open in [1]. These
partial answers give further support for conjecture $(*)$ from [1] on the set
of associated primes of MDLCMs. In addition, and also inspired by ideas from
Z\"oschinger, we prove some non-finiteness results of local cohomology.
