I understand you have done your setups correcrly, while raising the PO the Destination Organization should be your Inventory Org.
Define Project-Related Transaction Types in Oracle Inventory
In Oracle Inventory, create one or more transaction types that are enabled for project use. See Defining and Updating Transaction Types, Oracle Inventory User's Guide
Integrating Projects with Inventory without Project Manufacturing
You can implement Inventory to Projects integration so that you can issue from inventory to projects without installing Project Manufacturing. To implement this
integration, follow these steps:
1. Enable Project Cost Collection. In the Organization Parameters window in Oracle Inventory, enable the Project Cost Collection Enabled box.
2. Create a Project-Enabled Transaction Type. See: Define Project-Related Transaction Types in Oracle Inventory,
3. Set the INV: Project Miscellaneous Transaction Expenditure Type Profile Option.
In Oracle Inventory, set the value of this profile option to User Entered. With this setting, You must enter expenditure types for project miscellaneous transactions.
4. Create an Inventory Expenditure Type. In Oracle Projects, create an expenditure type with the transaction type class Inventory
The System allows you to create a PO with multiple distributions for the same line & shipment. That means you could have multiple project & tasks distributions. When you enter a receipt transaction system expect you to select the project and task that you are receiving for, since that may be not be a uniqe value.