clockgc
There is no relationship.
FP - Scheduled by USCIS. Some of the older cases has requested FP. Valid for 15 Months (If I remember correctly)
EAD - Valid for 1 year. Not required by H1b holder if H1B is valid, but required by spouse to work, or H1B holder to have additional job. Has to be current to be used with AC21 portability.
AP - Re-entry permit into US, valid for 1 year. Not required to have one, but it is good if you want to travel outside US, or in case of emergency.
Depending on the status of the GC process, will determine what you need.
If the other members want to add or correct me, please feel free. This is just my interpretation and not the law...