You can use webhook in JIRA to do a post REST call onto the BitBucket server. The webhook call can be set to be triggered only on the "sprint closed" event.
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Sample here
This API can also be invoked via a user-centric URL when addressing repositories in personal projects.
Create a new pull request between two branches. The branches may be in the same repository, or different ones. When using different repositories, they must still be in the same {@link Repository#getHierarchyId() hierarchy}.
The authenticated user must have REPO_READ permission for the "from" and "to"repositories to call this resource.
Example request representations:
{
    "title": "Talking Nerdy",
    "description": "It’s a kludge, but put the tuple from the database in the cache.",
    "state": "OPEN",
    "open": true,
    "closed": false,
    "fromRef": {
        "id": "refs/heads/feature-ABC-123",
        "repository": {
            "slug": "my-repo",
            "name": null,
            "project": {
                "key": "PRJ"
            }
        }
    },
    "toRef": {
        "id": "refs/heads/master",
        "repository": {
            "slug": "my-repo",
            "name": null,
            "project": {
                "key": "PRJ"
            }
        }
    },
    "locked": false,
    "reviewers": [
        {
            "user": {
                "name": "charlie"
            }
        }
    ]
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i tried curl -u user:pwd -H "Content-Type: application/json" https://localhost:7990/rest/api/1.0/projects/TES/repos/myrepo/pull-requests -X POST --data '{"title":"test","description":"test","fromRef":{"id":"refs/heads/master","repository":{"slug":"test-repo","name":null,"project":{"key":"myProject"}}},"toRef":{"id":"refs/heads/dev","repository":{"slug":"myrepo","name":null,"project":{"key":"TES"}}}}'
 
But it doesn't work
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