Fall asleep in civics class, did we? LOL!
See: Impeachment
The House brings impeachment charges against federal officials as part of its oversight and investigatory responsibilities. Individual Members of the House can introduce impeachment resolutions like ordinary bills, or the House could initiate proceedings by passing a resolution authorizing an inquiry. The Committee on the Judiciary ordinarily has jurisdiction over impeachments, but special committees investigated charges before the Judiciary Committee was created in 1813. The committee then chooses whether to pursue articles of impeachment against the accused official and report them to the full House. If the articles are adopted (by simple majority vote), the House appoints Members by resolution to manage the ensuing Senate trial on its behalf. These managers act as prosecutors in the Senate and are usually members of the Judiciary Committee. The number of managers has varied across impeachment trials but has traditionally been an odd number. The partisan composition of managers has also varied depending on the nature of the impeachment, but the managers, by definition, always support the House's impeachment action.
Now, you may be happy to have Congressional Republicans sitting on their hands instead of their sworn duty, but I prefer to hold their feet to the fire.
You didn’t say “impeach” or “prosecute”, you said “prosecute”. Words mean things. I didn’t have to go to a civics class to learn that, I learned it in Kindergarten.