You can't use personalization strings for the email when using RMM because it does not know which DE that information appears in. Personalization looks like it would work for the Forward Name: %%ReplyToName%% but definitely not for the %%ReplyToEmail%%.
A dynamic solution for forwarding that works with your RMM (Reply Mail Management) settings is to designate custom values in a Data Extension and then use the 'Lookup' function to lookup the values found in the data extension and insert the entire Lookup function in the Name and Address fields of your dynamic sender profile.
so for example
Step 1 - Create your email
Step 2 - Create your data extension with the custom forwarding fields
create the data extension: 'CustomForwardDataExt'
create the email address field: 'EmailAddress'
create the field for From Name: 'ForwardEmailName'
create the field for From Email Address: 'ForwardEmailAddress',
create a field column named "Group" with a default of "A" so you can do a lookup function
you'll want to populate this with some test data and it will serve as your target audience as well as contain the the forward information for any replies that receives the email.
Step 3 - Create your dynamic sender profile
Click in the Admin section and then under "send management" section in the left panel click on 'Sender Profile'. When creating a sender profile be sure to check the box for "Custom Reply Mail Management Settings" and then the radio button that says "Use specified information"
Step 4 - Create your 'user initiated send' or 'triggered send' and designate your sender profile
a) Select the email you wish to send from Step 1
b) Select the target audience list from Step 2.
c) Under the "Send Classification" area, check the box that says "Override Sender Profile with" and select the Sender Profile from the drop down menu that you created in Step 3.
When you receive the email test and click reply, you'll see the RMM functionality display it's usual reply-fe5b2823892899qads1-011_HTMLemail@example.com (i.e.) and also see the From Name populate the data from the 'CustomForwardDataExt' data extension.
Any responses to this will forward to your designated 'ForwardEmailAddress' value from your data extension.