Please post a picture of your setup. Almost surely , the chrome sleeve you are talking about MUST be removed. If may in fact be attached to the stem you need to remove. If you can post some pics of the handles and the wall setup, we can provide more details.
There are many, many brands and models which are similar to the example you posted, so don't buy any replacements until we pin that down. None of this stuff is "generic". You must get the specific part for your make and model.