No, if you have any dashboards you will have to go about creating something equivalent in Dynatrace. The two products handle dashboards very differently so there would not be a way to do a simple/automatic migration. Likewise the data itself is stored and handled differently so there is not a way to just migrate that into the stores that Dynatrace uses.
You can always keep your old appmon data around for a while if you need it but I haven't seen cases where that has been necessary. When you convert to Dynatrace you should think through your AppMon use cases and such to make sure you make any configs so as not to have gaps but the data itself will need to start over as it is a totally new solution.