We present a coordinated campaign of observations to monitor the brightness of the James Webb Space Telescope (JWST) as it travels toward the second Earth-Sun Lagrange point and unfolds using the network ofUnistellar digital telescopes. Those observations collected by citizen astronomers across the world allowed us to detect specific phases such as the separation from the booster, glare due to a change of orientation after a maneuver, the unfurling of the sunshield, and deployment of the primary mirror. After deployment of the sunshield on January 6 2022, the 6-h lightcurve has a significant amplitude and shows small variations due to the artificial rotation of the space telescope during commissionning. These variations could be due to the deployment of the primary mirror or some changes in orientation of the space telescope. This work illustrates the power of a worldwide array of small telescopes, operated by citizen astronomers, to conduct large scientific campaigns over a long timeframe. In the future, our network and others will continue to monitor JWST to detect potential degradations to the space environment by comparing the evolution of the lightcurve.