Ensure that your Jenkins server has the necessary tools installed to interact with PostgreSQL. This includes the `psql` command-line tool. You can install it using the package manager relevant to your operating system, for example, `apt-get install postgresql-client` on Ubuntu.

Set up a Jenkins job that will execute the series of commands necessary to extract and transfer data. This job can be a Freestyle project or a Pipeline project, depending on your preference and the complexity of the tasks.

Identify the data you want to move from Jenkins. This could be logs, build artifacts, or other data generated by Jenkins jobs. Use shell commands, Jenkins environment variables, or scripts to extract this data and save it to a file format suitable for PostgreSQL (e.g., CSV).

Format the extracted data if necessary to ensure it matches the schema of the target PostgreSQL tables. You might need to use shell scripting or command-line tools like `sed` or `awk` to clean or transform the data into the right structure.

Verify that Jenkins can access your PostgreSQL database. This will require setting up network permissions and ensuring that the necessary credentials (username, password, host, database name) are available in Jenkins. Store these credentials securely using Jenkins credentials management.

Use the `psql` command within your Jenkins job to load the data into PostgreSQL. This can be done using SQL commands or the `\copy` command if you're dealing with CSV files. For example:
```bash
psql -h your_host -U your_user -d your_database -c "\copy your_table FROM 'path_to_your_file.csv' CSV HEADER"
```
Include the `psql` command in your Jenkins job configuration, ensuring it uses the stored credentials.

Once the data transfer is complete, include a step in your Jenkins job to verify that the data has been correctly transferred. This can involve running a simple count query on PostgreSQL to check the number of rows, or more complex validations depending on your requirements. You can execute verification commands using `psql` and check the output.

By following these steps, you should be able to move data from Jenkins to a PostgreSQL destination without relying on third-party connectors or integrations.