It would be great if rather than passing connections down to child objects through form rules, one could check a box on a connection that locks a connection field to the value of the same field in a parent object. This would be great for scenarios where the child will always have the same connected object record as the parent and save a lot of form rule programming time.
Another method might be to allow the 'connection values ' to be accessible in text equations like other types of fields are.
Then one could sent a text formula value in the child object to display the field value of the parent's connection field and then make a conditional rule on the child's corresponding connection object "If 'text formula value' is 'not blank' set 'Connection to "text formula value."