Select the feature to which the dimension belongs, right click and choose Edit. The dimension you want to place on the layer should be showing.
Edit the properties of the layer (while the dimension is still on the screen), and place the mouse over the dimension, right click and choose "Pick from list". The dimension should show up on this list, select it and press OK. The dimension should now be on the layer.
You can also change the dimension's symbol (i.e. from d752 to layer_dim1) and create a rule based layer to automatially add dimensions with these names (i.e. Look For: Dimension, Name == layer_dim*).