From the either account but preferably the admin account ( I will assume you are in the Admin account) you can go to the users folders.
Select the the managed account home folder.
use cmd + i to get the info panel for the folder.
At the bottom you will see the allowed access to the folder.
This should show read & write for that user, and no access for everyone.
Click the padlock and enter your admin details.
Now click the + button and either choose your Admin account name.
The admin account should now be added to the list.
Now change its access to read & write.
You should now from the Admin account be able to open the managed user account's folder but not any folder inside.
You now have a choice. Depending on what you want.
If for example you want only to access the Documents folder and all the files and folders enclosed. Then repeat the process above Part 1 for the documents folder.
But this time, in the info panel for the documents folder, after you have completed the above Part 1 on it. You will see a action button (Cog) at the bottom of the panel below the list.
Click the button and then the
Apply to enclosing items…
When you confirm, all the items in Documents folder will replicate the access given to the Documents folder.
Or you can do the above by drilling down to only the folders you are interested in using Part 1 and the final folder in that chainPart 1 & Part 2
Or of cause you can just do chainPart 1 & Part 2 on the home folder.
But I personally would just do the folders I need.