I have a 04 ford expidition woth a p0620 and a batt. Light that is always on took it to a auto store and had the battery ,the starter and the (new) battery , and alternator checked and they said everything passed just replaced the fusible link and about to replace the alternator would that fix the p0620 or if I replaced the whole PCM would that fix it suggestions needed and appreciated running out of ideas

 

There are some pitfalls involved if you choose to replace the PCM, it will need to be programmed to your individual vehicle and you have a choice there.
You can purchase a PCM already programmed to your vehicle VIN which you supply to the selling co, or have it programmed locally or if not done , the vehicle may not even start and now road service will be required.
In addition , if you decide to reinstall the original PCM, the security system will be confused and it may not start now.

The problem needs to be thoroughly checked by someone who is familiar with the charging system before replacing anything.

Sometimes a poor connection can produce these problems and the connection gets moved in the process of replacing parts and a temporary fix results.

A good shop knows what to check and where and is worth considering.