This is the 14940th most frequent Russian word.
подключившись
"Having connected" or "by connecting."
Here, 'подключившись' is used as a perfective gerund reflecting the completion of an action (connecting) prior to another action (downloading).
Подключившись к интернету, мы смогли скачать нужные файлы.
Having connected to the internet, we were able to download the necessary files.
In this sentence, 'подключившись' emphasizes the manner in which the secondary action (joining) occurs.
Она вошла в конференцию, подключившись через приложение на телефоне.
She joined the conference by connecting through the app on her phone.
Here, 'подключившись' denotes an initiating action, setting the stage for the following event (starting work).