See:

heir/heirs who take over the rights and obligations of the deceased partner. A minor heir is represented by his guardian according to law; in case of several heirs, they are represented by one who is duly authorized by the remainder. In case of a deceased partner that had more than one shares and whose heirs that fulfill the.
http://www.serrescoopbank.gr/en/images/charter_english.pdf

In any event of change of the PEC box Holder, the transferee or party entitled will take over the rights and obligations of the deceased. Term and withdrawal. The PEC service will feature the same term as the undersigned Vianova agreement, of which the PEC box constitutes an additional service. The Client can withdraw ...
https://www.welcomeitalia.it/en/general-terms-and-conditions...


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Note added at 21 mins (2018-02-15 13:29:14 GMT)
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You could also day. ""inherit the rights and obligations of the deceased". See:

They need to know all of their options in avoiding foreclosure and/or what to expect during the foreclosure process. This may include the children, grand children, great grand children, etc. The beneficiaries of the estate will inherit the rights and obligations of the deceased. Lawyers in Munich will be able to explain in detail ...
http://tmnhtu.com/feldman-law-center-foreclosure-ethics-aler...


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Note added at 30 mins (2018-02-15 13:37:39 GMT)
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You could also say, “assume the rights and obligations of the deceased”. See:

As a rule, the inheritors shall assume the rights and obligations of the deceased. In other words, the property and all other rights are transferred to the inheritors; and the legal duties and obligations not of a personal nature are also assumed by the inheritors. However, sometimes the deceased might have had many duties ...
https://books.google.gr/books?id=84bfG5_1T5oC&pg=PA147&lpg=P...

As a rule, the heir(s) must sign a new SMP agreement within six months of the previous SMP's death and thus assume the rights and obligations of the deceased SMP. The death must be proven by means of a death certificate. Should there be a will granting the SMP Agreement as part of the deceased's inheritance, ...
https://www.srkcoin.com/terms-condition

As a rule, the heir(s) must sign a new partnership agreement within six months of the previous Representative's decease whereby they will assume the rights and obligations of the deceased Representative. The death must be proven by means of a death certificate. Should there be a will granting the partnership agreement ...
http://www.qneurope.com/en/footer/term_of_use/

https://www.google.co.uk/search?ei=j4uFWv07ytbAAs21m7gH&q=as...