Hi Krisztian,
Thanks for posting in the community. We are happy to help you.
Microsoft does provide a "Save as" button or a "Save to OneDrive" button for users to save the file in an email to their OneDrive directly (as shown in the screenshot below). However, the short answer to your query is "no", and in this special situation, to save it to your OneDrive, you will have to download a copy locally, and then upload it to OneDrive.
The root cause is due to the way your colleague inserted the document in the email (your colleague used the shared link to insert the document in the email, and she set the shared link to "Can View" (View Only permission), which causes you to have to download a copy locally, and then upload it to OneDrive.



Please note that the sender has two ways to insert a document into the email. One is to attach the file to the email and another is to insert the shared link of the file to the email. Also, when the sender inserts the shared link of the file, he can set different permissions to the link. If your colleague attached the OneDrive, then you can click "Save to OneDrive" to save the file to OneDrive directly. If your colleague attached the shared link of the file, but set the link to "Can Edit", then you can click File> Save as to save as the file to your OneDrive directly.

We look forward to your response. Thanks for your cooperation.
Sincerely,
George | Microsoft Community Moderator