Hi Heeral,
Unfortunately, the changes you want to make are on the Resource object. So we can't use an auto-start process to xog in these rights every time your Functional Manager attribute is changed.
However, there is another approach you can use. You will need to create a gel script process that determines which Functional managers have been changed or added since the last time you ran this job. Then you could use the gel script to create a Resource Write xog file to xog these rights for that user into the new Functional Manager resource.
That process could then be run via the Execute a Process job to run on a scheduled basis.
This would take some know-how with gel scripts. But, if you don't have the in-house people who are capable of creating this type of process, you could engage CA Services or a partner to create this for you.
This is just a general approach that would accomplish what you want.