Looking to create an API between Vend and Storefeeder

Vend is an EPOS system that we us eon our front counter till and storefeeder is our order and stock management system.
Both systems have full API documentation.

We need to be able to following:
Sync stock, price, inventory count from storefeeder to vend.
Create new products from storefeeder to vend.
Create a sale from vend to storefeeder this will deduct the stock of the sale in storefeeder.

Here are the links to the companies API documentations hope this helps.
Storefeeder: rest.storefeeder.com
Vend: https://docs.vendhq.com/docs/client-api-reference

We have our own PHP server.
I hope this is enough info for you to have an idea on what im looking to do?
Any questions please let me know.