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If he has left the house to you as opposed to giving you a right to remain in the house until you pass away then the house will pass to you upon his death subject to the mortgage being repaid. The will shall stipulate if the mortgage is to be paid from the remainder of his estate (his residuary estate) before that passes to his sons. If that is the case then the mortgage will be settled from his other assets and then transferred to you.
Your joint bank accounts will pass to you by survivorship.
The danger is that if he now subsequently changes his will so that you do not inherit the property you will be left with the prospect of claiming and possibly litigating that you should have a share of the equity in the property on the basis of your mortgage contributions. This can be expensive.
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In that case the mortgage will be repaid by the insurance policy proceeds upon death, the mortgage will be removed from the registered title to the property and this will then be transferred in to your sole name.
The joint accounts will simply be transferred in to your name upon the banks having been furnished with the death certificate of your partner.
The sons will only be able to make a further claim on the estate if they make claim within 6 months of the grant of probate being issued and they were to some extent financially dependent upon their father before his death. The Court would consider what is a reasonable financial provision to be made to them but if they are to receive relatively substantial amounts passing under the residuary estate then it will be much harder for them to claim.
The insurance policies will pay out according to the terms of the policies.
If the house is to pass to you absolutely after the mortgage has been repaid from an insurance policy then it will be yours to do as your wish. If you wish to leave it in the way you have mentioned in your most recent reply then it will be up to you to execute a Will based on those instructions.