Her birth index is to be found on Scotland’s people.

No marriage or death on Scotland’s People.

The following marriage was in England which might have been hers:

First name(s) SUSAN A
Last name MCMURDO
Marriage quarter 2
Marriage year 1911
Registration month -
MarriageFinder™ SUSAN A MCMURDO married one of these people
JOHN J SCOTT, ARTHUR E MADLE
District BRIGHTON
District number -
County Sussex
Country England
Volume 2B
Page 513
Record set England & Wales marriages 1837-2008
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Using the 1939 Register, there are 5 Susan Scotts in England in the Register but no Susan A Scott.

There was one Susan A Madle in the Register, listed as a widow, living on her own and born on 25 Sep 1889.  The Madle name was struck out and Trott added, to indicate that she subsequently changed her name, through marriage or otherwise.

My vote is that she married Arthur E Madle.  But no Madle children were born with a McMurdo mother’s maiden name.  Though she had no children living with her in 1939.
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In 1942 Susan A Madle married Arthur C Trott:

First name(s) SUSAN A
Last name MADLE
Marriage quarter 2
Marriage year 1942
Registration month -
MarriageFinder™ SUSAN A MADLE married
ARTHUR C TROTT
Spouse's last name TROTT
District BATTERSEA
District number -
County London
Country England
Volume 1D
Page 729
Record set England & Wales marriages 1837-2008
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Susan Agness Trott then died in 1971, with the same birth date as on the 1939 Register:

First name(s) SUSAN AGNES
Last name TROTT
Gender Female
Birth day 25
Birth month 9
Birth year 1889
Age -
Death quarter 1
Death year 1971
District HASTINGS
County Sussex
Volume 5H
Page 1186
Country England
Record set England & Wales deaths 1837-2007

The probate index gives her death date as 3 Feb 1971 but no executor info so can’t guess at her beneficiaries, if any.  As I can’t see any sign of any children, I will not bother with getting her will.
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