In this paper we prove that maximal H-monotone operators class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302371&_mathId=si1.gif&_user=111111111&_pii=S0362546X16302371&_rdoc=1&_issn=0362546X&md5=a321c42f468ea972515c31bfa7818aa2" title="Click to view the MathML source">T:Hn⇉V1class="mathContainer hidden">class="mathCode"> whose domain is all the Heisenberg group class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302371&_mathId=si2.gif&_user=111111111&_pii=S0362546X16302371&_rdoc=1&_issn=0362546X&md5=e72ca78a98fd5252861c18df0710b991" title="Click to view the MathML source">Hnclass="mathContainer hidden">class="mathCode"> are locally bounded. This implies that they are upper semicontinuous. As a consequence, maximal H-monotonicity of an operator on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302371&_mathId=si2.gif&_user=111111111&_pii=S0362546X16302371&_rdoc=1&_issn=0362546X&md5=e72ca78a98fd5252861c18df0710b991" title="Click to view the MathML source">Hnclass="mathContainer hidden">class="mathCode"> can be characterized by a suitable version of Minty’s type theorem.