Here's an example Java program to check if a string is a valid shuffle of two distinct strings:

public class StringShuffleChecker {
    public static void main(String[] args) {
        String str1 = "abc";
        String str2 = "def";
        String shuffle = "adbecf";

        if (isShuffle(str1, str2, shuffle)) {
            System.out.println(shuffle + " is a valid shuffle of " + str1 + " and " + str2);
        } else {
            System.out.println(shuffle + " is not a valid shuffle of " + str1 + " and " + str2);
        }
    }

    public static boolean isShuffle(String str1, String str2, String shuffle) {
        if (str1.length() + str2.length() != shuffle.length()) {
            return false;
        }

        int i = 0, j = 0, k = 0;

        while (k < shuffle.length()) {
            if (i < str1.length() && str1.charAt(i) == shuffle.charAt(k)) {
                i++;
            } else if (j < str2.length() && str2.charAt(j) == shuffle.charAt(k)) {
                j++;
            } else {
                return false;
            }

            k++;
        }

        return true;
    }
}

This program uses an isShuffle method that takes three strings as input: str1, str2, and shuffle. The method returns true if shuffle is a valid shuffle of str1 and str2, and false otherwise.

To check if shuffle is a valid shuffle of str1 and str2, the isShuffle method first checks if the length of shuffle is equal to the sum of the lengths of str1 and str2. If not, the method returns false, indicating that shuffle cannot be a valid shuffle of str1 and str2.

The method then uses three pointers: i for str1, j for str2, and k for shuffle. It loops through each character of shuffle and checks if the character at k matches the character at either i or j. If the character matches the character at i, the method increments i. If the character matches the character at j, the method increments j. If the character does not match either i or j, the method returns false, indicating that shuffle cannot be a valid shuffle of str1 and str2.

If the method reaches the end of shuffle without finding any mismatches, it returns true, indicating that shuffle is a valid shuffle of str1 and str2.

In the main method, the isShuffle method is called with three strings: str1 contains the characters "abc", str2 contains the characters "def", and shuffle contains the characters "adbecf". If shuffle is a valid shuffle of str1 and str2, the program prints a message indicating that shuffle is a valid shuffle of str1 and str2. Otherwise, it prints a message indicating that shuffle is not a valid shuffle of str1 and str2.