I can recommend:

Basic German - A Grammar and workbook

Heiner Schenke and Karen Seago

I use this book with some of my students.

Unfortunately, I can't recommend a textbook for English speakers as I only used textbooks that were entirely in German but I'd lik to recommend a couple of good online resources:

Learn German with Deutsche Welle: <a href="https://www.dw.com/en/learn-german/s-2469" rel="noopener noreferrer" target="_blank">https://www.dw.com/en/learn-german/s-2469</a>;

Learn German with Jenny: <a href="https://www.youtube.com/watch?v=gz9JbZcfnrk&list=PL5QyCnFPRx0GxaFjdAVkx7K9TfEklY4sg" rel="noopener noreferrer" target="_blank">https://www.youtube.com/watch?v=gz9JbZcfnrk&list=PL5QyCnFPRx0GxaFjdAVkx7K9TfEklY4sg</a>;

Learn German with Anja: <a href="https://www.youtube.com/watch?v=MOtqMNKs0Jw&list=PLYzp2xhTw9W1Z9RvnCoveC0W7pkwUMHXy" rel="noopener noreferrer" target="_blank">https://www.youtube.com/watch?v=MOtqMNKs0Jw&list=PLYzp2xhTw9W1Z9RvnCoveC0W7pkwUMHXy</a>;

Don't hesitate to contact me, if you have questions about German. I'm a native German speaker and speak English fluently and Japanese on intermediate level.

I would then recommend German Grammar in Context by Routledge. The book is written in English. There are grammar exercises at the end of each chapter. It's not a A1 level textbook although I am pretty sure it encompasses all the grammar points that one should know at A1 level. Hope you like it! 🥰

About 20 years ago, my beginning German class at university used Deutsche Heute by Moeller.

I see that a newer edition is available on amazon.co.jp.

Thank you so much for useful information everybody! I really couldn't find any nice one by myself. Danke for taking your time! ฅʕ•ᴥ•ʔฅ゛