Here's the updated TypeScript code that stores the famous person's name in a variable and composes the message using the stored variables:
```typescript
const famous_person: string = "Albert Einstein";
const message: string = famous_person + ' once said, "A person who never made a mistake never tried anything new."';
console.log(message);
```
In this code, we create a variable called `famous_person` and assign the name of the famous person, "Albert Einstein", to it.
Then, we create another variable called `message` and compose the message by concatenating the `famous_person` variable with the quote using string concatenation (`+`) and including the necessary quotation marks and punctuation.
Finally, we use `console.log` to print the `message` variable, which contains the composed message, to the console.
When executed, this code will print the following message to the console:
```
Albert Einstein once said, "A person who never made a mistake never tried anything new."
```
The updated code allows for more flexibility by storing the famous person's name in a variable and composing the message using the stored variables.