If you want to claim the migration layer in Minecraft, you will first need to migrate your Java account to Microsoft. Once migrated, you will be able to equip your new cape through the option to do so in your profile on the Mojang website.
With that said, to migrate your Minecraft Java account to Microsoft, you will first need to log into your Mojang account.
Players can log into their Mojang accounts by heading to the official Mojang website and entering all of their information in the email and password options. You will also need to use the email you created in your Java account along with your password.
Once you’ve signed in, head over to your profile and look for a button that says move your account to begin the process of migrating your account to Microsoft.
First, you will need to confirm your email address. To do this, a code will be required that Mojang will send to the email in which you created the account. Take the code, enter it in the box that will appear right after you get the code.
Next, you will need to create a Microsoft and Xbox account. If you already have one for both of you, just log into your Microsoft account now, and your Java account will automatically be migrated and linked.
If you don’t have one yet, create one now for Microsoft and Xbox, and sign in with your Microsoft account to migrate your account from Java to Microsoft.
Once your account has been migrated, go back to your profile and you should see a layer change option with the migration layer below the list of options. Change the layer to the migration layer and then log into the Minecraft launcher using Microsoft by going back to the login page.
Press sign in with Microsoft and check all your Microsoft information to sign in. Afterward, you will have the cape permanently until you remove it from your character in Minecraft.