As a long-time iOS user and Chrome enthusiast, I appreciate how Google's browser delivers seamless cross-platform syncing. However, Apple's restrictions on third-party browsers have historically limited features like easy PDF saving—unlike Safari's direct integration with Books.
Good news: Recent Chrome updates for iOS change that. You can now save PDFs opened in Chrome straight to Books or the Files app on your iPhone or iPad. I've tested this extensively, and it's straightforward. Here's how.
Also read: How to Disable Suggested Articles in Chrome for iOS and Android Without Affecting Search
After opening a PDF in Chrome on your iPhone or iPad, tap the screen lightly. Look for the "OPEN IN" option at the bottom and select it.

Tip: If "OPEN IN" doesn't appear, update Chrome via the App Store—it's essential for this feature.
Chrome opens a dedicated Share sheet with PDF-specific actions, distinct from the standard browser Share button.

Choose "Copy to Books" to instantly load the PDF there, where you can annotate with built-in markup tools and share directly.
"Copy to Notes" adds it to a note, while AirDrop sends it as a link to nearby devices. For broader access, select "Save to Files."

This launches the Files app, letting you save to iCloud Drive, OneDrive, Google Drive, or any subfolder. Tap "Save," and it's done.

Saving to Books offers limited management, and cloud saves aren't local. For local storage, use the workaround below.
In Files, select "On My iPhone" or "On My iPad" (available with apps like Word, PowerPoint, or VLC installed).
If missing: How to Fix My iPhone or iPad Missing Folder Issue on iOS 11 Files App
These app folders enable local saving from Chrome. Note: This is a workaround—deleting the linked app removes files, so back up accordingly.

Files app integration provides robust management for all saved PDFs.
Open Files, navigate to your PDF, and tap to view using iOS's native preview—much like Books.

Annotate with familiar tools; changes save automatically on close.

To open in Adobe Acrobat Reader or similar, long-press the file, tap Share, and choose your app.

Easily move, rename, or tag PDFs across locations—iOS 11's Files app shines here.
Complete guide to the Files app: Top 10 Ways to Use the Files App on iOS Like a ProChrome on iOS no longer requires clunky workarounds like print menus or Safari switches for PDFs. Save directly to cloud or local folders effortlessly.
I've streamlined my workflow this way—try it and share your experience in the comments.