Looking on the internet deeply has found these results:

could have sent me a letter is the most popular phrase on the web.

could have written me letter 10 results on the web	could have sent me a letter 160 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Feb 16, 2016 ... "You could have sent me a letter. You could have called me," Aker said. The U.S. Marshals said later in court that they had the firepower ... Feb 16, 2016 ... “You could have sent me a letter. You could have called me,” Aker said. The U.S. Marshals said later in court that they had the firepower ... Feb 18, 2016 ... “You could have sent me a letter. You could have called me,” Aker reportedly said. He says he was ordered into the back of a truck and taken to ... ... they've decided that I'm not 'up to it' (which I certainly am not), I suppose they could have sent me a letter & that letter got lost in the post.

could have written me letter

10 results on the web

could have sent me a letter

160 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Feb 16, 2016 ... "You could have sent me a letter. You could have called me," Aker said. The U.S. Marshals said later in court that they had the firepower ...
Feb 16, 2016 ... “You could have sent me a letter. You could have called me,” Aker said. The U.S. Marshals said later in court that they had the firepower ...
Feb 18, 2016 ... “You could have sent me a letter. You could have called me,” Aker reportedly said. He says he was ordered into the back of a truck and taken to ...
... they've decided that I'm not 'up to it' (which I certainly am not), I suppose they could have sent me a letter & that letter got lost in the post.