Proceed as follows:
1. Enter transaction code: SE10
2. Next, click on Display
3. Locate your request under "Modifiable"
4. Click on the plus + next to the request to expand the node
5. Select the customizing task and then click on transport "Release Directly"
6. Wait till the customizing task is fully released.
7. Thereafter, select the main request and click again on the transport "Released Directly".
8.Once the request is fully released, give that number to your basis guys to transport to test system for you.
Reason I said give the request number to the basis group to transport is, that is their job and from reading of your question it seems you don't know much about transport so my advice is let the experts handle that.
9.Then go to STMS, and select your dev system and transport from there. Then you need to go to your test system and import there.