На компе файл создается, данные передаются в нужном порядке: сначала из файла Lion.avi.part1, потом из Lion.avi.part2 и тд

TreeMap<String,ByteArrayOutputStream> sortedFiles = new TreeMap<>(files);

TreeMap<String, Integer> map = new TreeMap<>();
map.put("Lion.avi.part37", 37);
map.put("Lion.avi.part2", 2);
map.put("Lion.avi.part1", 1);
map.put("Lion.avi.part12", 12);
map.put("Lion.avi.part4", 4);

map.entrySet().forEach(System.out::println);

public class Solution {
    public static void main(String[] args) throws IOException {

        HashMap<String, ByteArrayOutputStream> files = new HashMap<>();

        String fileName = "/Users/user/Desktop/lessons/file.txt";
        String fileName2 = "/Users/user/Desktop/lessons/file4.txt";


        try (FileReader file = new FileReader(fileName)) {
            ByteArrayOutputStream writer = new ByteArrayOutputStream();
            while (file.ready()) {
                writer.write(file.read());
            }
            files.put(fileName, writer);
        }
        try (FileReader file2 = new FileReader(fileName2)) {
            ByteArrayOutputStream writer = new ByteArrayOutputStream();
            while (file2.ready()) {
                writer.write(file2.read());
            }
            files.put(fileName2, writer);
            writer.close();
        }

        TreeMap<String, ByteArrayOutputStream> sortedFiles = new TreeMap<>(files);
        System.out.println(sortedFiles);

        File f = new File("/Users/user/Desktop/lessons/Lion.txt");

        if (f.createNewFile())
            System.out.println("File created");
        else
            System.out.println("File already exists");
        try (FileWriter file1 = new FileWriter(f)) {
            for (Map.Entry<String, ByteArrayOutputStream> entry : sortedFiles.entrySet()) {
                file1.write(entry.getValue().toString());

            }
        }

    }
}

String fileName = "/Users/user/Desktop/lessons/file11.txt";
String fileName2 = "/Users/user/Desktop/lessons/file4.txt";