This is the 7276th most frequent Russian word.
воспользовавшись
"Having taken advantage (of)" or "using (something)."
The word 'воспользовавшись' here means 'by using' or 'taking advantage of.' It introduces the method or means by which the action was accomplished.
Мы смогли достичь вершины, воспользовавшись коротким маршрутом.
We managed to reach the summit by taking advantage of the shorter route.
In this sentence, 'воспользовавшись' denotes the tool or method (email) used to complete the action of contacting her friend.
Она решила связаться с другом, воспользовавшись электронной почтой.
She decided to contact her friend by using email.
Here, 'воспользовавшись' illustrates the act of seizing or using an opportunity (the unexpected invitation) to achieve a specific outcome (seeking shelter).