Hello MinnieValerie,
Thanks for your post to Apple Support Communities. We wanted to provide some guidance about your questions regarding the messages not going through your contact with an Android phone. Based on what you described, we'd advise you to connect with them to check on their end. When someone is blocked, whether it's an overall block or specific attachments like a screenshot, it is from the phone number sending the block message.
You wouldn't have any settings to adjust on your end to be able to send specific attachments to a contact, even with an Android phone. They may have restrictions set to not receive attachments, screenshots, or files of a certain size. It could also be something they have set specifically for your phone number.
We'd advise testing with another Android user to confirm it is with that one contact. If you have any other questions, reply back here.
Best regards.